Updated on 2024/10/07

写真b

 
GEISSER, Thomas H.
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Graduate School of Science Doctoral Program in Mathematics
Graduate School of Science Master's Program in Mathematics
Title*
Professor
Degree
修士 （ ボン大学 ） / 博士 （ ムンスター大学 ） / Diplom （ Rheinische Friedrich-Wilhelms-Universitaet Bonn ） / Dr. rer. nat. （ Westfaelische Wilhelms Universitaet Muenster ）
Contact information
Mail Address
Research Theme*

  • 代数多様体(整数係数又は有理数係数の多項式の系の解集合)を研究する数論幾何学が研究テーマである。例えば、局所的な情報から定義されるゼータ関数と大域的に定義されるコホモロジー群という二つの不変量を比較することによって代数多様体に関する情報を得る。特にモチビック・コホモロジーと高次Ｋ—理論という不変量に対して興味がある。

    • Campus Career*
    • 4 2015 - Present 
      College of Science   Department of Mathematics   Professor
    • 4 2015 - Present 
      Graduate School of Science   Master's Program in Mathematics   Professor
    • 4 2015 - Present 
      Graduate School of Science   Doctoral Program in Mathematics   Professor
     

    Research Areas

    • Natural Science / Algebra

    Research History

    • 4 2015 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Professor

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    • 4 2010 - 3 2015 
      Nagoya University   School of Science Department of Mathematics   Professor

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      Country：Japan

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    Education

    • 10 1990 - 5 1994 
      Westfaelische-Wilhelms Universitaet Muenster   Mathematics   Mathematics

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      Country： Germany

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    • 10 1985 - 9 1990 
      Universität Bonn   Mathematics

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      Country： Germany

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    Awards

    • 4 2021  
      Humboldt Foundation  Humboldt Research Fellowship 

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    • 2000  
      Alfred P. Sloan Foundation  Sloan Fellowship 

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    Papers

    • A Weil-etale version of the Birch and Swinnerton-Dyer formula over function fields. Peer-reviewed

      Thomas H. Geisser, Takashi Suzuki

      J. Number Theory208   367 - 389   1 1 2020

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      Language：English   Publishing type：Research paper (scientific journal)  

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    • Comparing the Brauer group to the Tate-Shafarevich group. Peer-reviewed

      Thomas H. Geisser

      J. Inst. Math. Jussieu19 ( 202 ) 965 - 970   1 1 2020

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      Language：English   Publishing type：Research paper (scientific journal)  

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    • Hasse principles for etale motivic cohomology Peer-reviewed

      Thomas H. Geisser

      Nagoya Math. Journal236   63 - 83   1 1 2019

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      Language：English   Publishing type：Research paper (scientific journal)  

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    • Poitou-Tate duality for arithmetic schemes Peer-reviewed

      Thomas H. Geisser, A.Schmidt

      Compositio Math.154   2020 - 2044   1 1 2018

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      Language：English   Publishing type：Research paper (scientific journal)  

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    • On the structure of \'etale motivic cohomology Peer-reviewed

      Thomas H. Geisser

      Journal Pure Applied Algebra221   1614 - 1628   1 1 2017

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    • Some remarks on etale motivic cohomology Peer-reviewed

      Thomas Geisser

      Journal Pure Applied Algebra   1 1 2017

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    • Tame class field theory for singular varieties over finite fields Peer-reviewed

      Thomas Geisser, Alexander Schmidt

      JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY19 ( 11 ) 3467 - 3488   2017

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：EUROPEAN MATHEMATICAL SOC  

      Schmidt and SpieB described the abelian tame fundamental group of a smooth variety over a finite field by using Suslin homology. In this paper we show that their result generalizes to singular varieties if one uses Weil-Suslin homology instead.

      DOI： 10.4171/JEMS/744

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    • Parshin's Conjecture and Motivic Cohomology with Compact Support Peer-reviewed

      Thomas Geisser

      Comment. Math. Univ. Sancti Pauli   1 1 2016

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    • TAME CLASS FIELD THEORY FOR SINGULAR VARIETIES OVER ALGEBRAICALLY CLOSED FIELDS Peer-reviewed

      Thomas Geisser, Alexander Schmidt

      DOCUMENTA MATHEMATICA21   91 - 124   2016

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：UNIV BIELEFELD  

      Let X be a separated scheme of finite type over an algebraically closed field k and let m be a natural number. By an explicit geometric construction using torsors we construct a pairing between the first mod m Suslin homology and the first mod m tame etale cohomology of X. We show that the induced homomorphism from the mod m Suslin homology to the abelianized tame fundamental group of X mod m is surjective. It is an isomorphism of finite abelian groups if (m, char(k)) = 1, and for general m if resolution of singularities holds over k.

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    • Applications and conjectures in motivic cohomology theory Invited Peer-reviewed

      Geisser Thomas

      Sugaku67 ( 3 ) 225 - 245   1 1 2015

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      Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：The Mathematical Society of Japan  

      DOI： 10.11429/sugaku.0673225

      CiNii Article

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    • Rojtman's theorem for normal schemes Peer-reviewed

      Thomas Geisser

      MATHEMATICAL RESEARCH LETTERS22 ( 4 ) 1129 - 1144   2015

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：INT PRESS BOSTON, INC  

      We show that Rojtman's theorem holds for normal schemes: For every reduced normal scheme X of finite type over an algebraically closed field k, the torsion subgroup of the zero'th Suslin homology is isomorphic to the torsion subgroup of the k-rational points of the albanese variety of X (the universal object for morphisms to semi-abelian varieties).

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    • HOMOLOGICAL DESCENT FOR MOTIVIC HOMOLOGY THEORIES Peer-reviewed

      Thomas Geisser

      HOMOLOGY HOMOTOPY AND APPLICATIONS16 ( 2 ) 33 - 43   2014

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：INT PRESS BOSTON, INC  

      The purpose of this paper is to give homological descent theorems for motivic homology theories (for example, Suslin homology) and motivic Borel-Moore homology theories (for example, higher Chow groups) for certain hypercoverings.

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    • On a conjecture of Vorst Peer-reviewed

      Thomas H. Geisser, L. Hesselholt

      Math. Zeitschrift270   445 - 452   1 1 2012

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    • DUALITY FOR Z-CONSTRUCTIBLE SHEAVES ON CURVES OVER FINITE FIELDS Peer-reviewed

      Thomas Geisser

      DOCUMENTA MATHEMATICA17   989 - 1002   2012

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：UNIV BIELEFELD  

      We prove a duality theorem for Weil-etale cohomology of Z-constructible sheaves on curves over finite fields.

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    • Finite generation conjectures for motivic cohomology theories over finite fields Peer-reviewed

      Thomas Geisser

      REGULATORS571   153 - 165   2012

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      Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：AMER MATHEMATICAL SOC  

      For varieties over finite fields, we relate motivic cohomology and Weil-etale cohomology by an intermediate cohomology theory. All theories are conjecturally finitely generated, and we examine their relationship.

      DOI： 10.1090/conm/571/11326

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    • On relative and BI-relative algebraic K-theory of rings of finite characteristic Peer-reviewed

      Thomas Geisser, Lars Hesselholt

      Journal of the American Mathematical Society24 ( 1 ) 29 - 49   1 2011

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      Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.1090/S0894-0347-2010-00682-0

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    • On the vanishing of negative K-groups Peer-reviewed

      Thomas Geisser, Lars Hesselholt

      MATHEMATISCHE ANNALEN348 ( 3 ) 707 - 736   11 2010

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

      We show that for a d-dimensional scheme X essentially of finite type over an infinite perfect field k of characteristic p > 0, the negative K-groups K(q) ( X) vanish for q < -d provided that strong resolution of singularities holds over the field k.

      DOI： 10.1007/s00208-010-0500-z

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    • Arithmetic homology and an integral version of Kato's conjecture Peer-reviewed

      Thomas Geisser

      JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK644   1 - 22   7 2010

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：WALTER DE GRUYTER & CO  

      We define an integral Borel-Moore homology theory over finite fields, called arithmetic homology, and an integral version of Kato homology. Both types of groups are expected to be finitely generated, and sit in a long exact sequence with higher Chow groups of zero-cycles.

      DOI： 10.1515/CRELLE.2010.050

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    • Duality via cycle complexes Peer-reviewed

      Thomas H. Geisser

      Ann. of Math.172   1095 - 1126   1 1 2010

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    • On Suslin's singular homology and cohomology Peer-reviewed

      Thomas H. Geisser

      Documenta Math.   223 - 249   1 1 2010

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    • The affine part of the Picard scheme Peer-reviewed

      Thomas Geisser

      COMPOSITIO MATHEMATICA145 ( 2 ) 415 - 422   3 2009

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：CAMBRIDGE UNIV PRESS  

      We describe the maximal torus and maximal unipotent subgroup of the Picard variety of a proper scheme over a perfect field.

      DOI： 10.1112/S0010437X08003710

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    • Bi-relative algebraic K-theory and topological cyclic homology Peer-reviewed

      Thomas Geisser, Lars Hesselholt

      INVENTIONES MATHEMATICAE166 ( 2 ) 359 - 395   11 2006

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

      DOI： 10.1007/s00222-006-0515-y

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    • On the $K$-theory and topological cyclic homology of smooth schemes over a discrete valuation ring Peer-reviewed

      Thomas H. Geisser, L. Hesselholt

      Trans. AMS358   131 - 145   1 1 2006

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    • The de Rham-Witt complex and p-adic vanishing cycles Peer-reviewed

      Thomas Geisser, Lars Hesselholt

      Journal of the American Mathematical Society19 ( 1 ) 1 - 36   1 2006

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      Language：English   Publishing type：Research paper (scientific journal)  

      DOI： 10.1090/S0894-0347-05-00505-9

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    • On the K-theory of regular local $F_p$-algebras Peer-reviewed

      Thomas H. Geisser

      Topology45   475 - 493   1 1 2006

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    • Arithmetic cohomology over finite fields and values of zeta-functions Peer-reviewed

      Thomas H. Geisser

      Duke Math. J.133   27 - 57   1 1 2006

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    • Motivic cohomology, algebraic K-theory and topological cyclic homology Peer-reviewed

      Thomas H. Geisser

      Handbook of K-theory   193 - 243   1 1 2005

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer  

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    • Motivic Cohomology over Dedekind rings Peer-reviewed

      Thomas H. Geisser

      Math. Z.248   773 - 794   1 1 2004

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    • Weil-etale cohomology over finite fields Peer-reviewed

      Thomas H. Geisser

      Math. Ann.330   665 - 692   1 1 2004

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    • The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky Peer-reviewed

      Thomas H. Geisser, M.Levine

      J. reine angew. Math.530   55 - 103   1 1 2001

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    • The K-theory of fields of characteristic p Peer-reviewed

      Thomas H. Geisser, M.Levine

      Invent. Math.139   459 - 493   1 1 2000

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    • Topological cyclic homology of schemes Peer-reviewed

      Thomas H. Geisser, L. Hesselholt

      Proc. Symp. Pure Math.67   41 - 88   1 1 1999

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    • Tate's conjecture, algebraic cycles and rational K-theory in characteristic p Peer-reviewed

      Thomas H. Geisser

      K-Theory13   109 - 122   1 1 1998

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    • Applications of de Jong's theorem on alterations Peer-reviewed

      Thomas H. Geisser

      Progr. Math.,181   299 - 314   1 1 1997

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    • p-adic K-theory of Hecke characters of imaginary quadratic fields Peer-reviewed

      Thomas H. Geisser

      Duke Math. J.86   197 - 238   1 1 1997

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    • On K3 of Witt vectors of length two over finite fields Peer-reviewed

      Thomas H. Geisser

      K-Theory12   193 - 226   1 1 1997

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    • Galoiskohomologie reeller halbeinfacher algebraischer Gruppen Peer-reviewed

      Thomas H. Geisser

      Abh. Math. Sem. Univ. Hamburg61   231 - 242   1 1 1991

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    Misc.

    Research Projects

    • Arithmetic algebraic geometry

      Special Coordination Funds for Promoting Science and Technology 

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      5 1994 - 3 2031

      Grant type：Competitive

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    • Application of the theory of motives to various cohomology theories and period integral

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      Terasoma Tomohide

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      4 2015 - 3 2020

      Grant number：15H02048

      Grant amount：\27950000 （ Direct Cost: \21500000 、 Indirect Cost：\6450000 ）

      We study special functions and period integrals arising from special varieties, such as hypergeometric functions, multiple polylogarithm functions, multiple zeta values, etc. from a geometric point of view. We give explicit presentation of geometric objects such as inverse period functions, and unexpected relation between them. We try to find geometric origin lying behind observed phenomena. Our strategy is to apply modern strong algebra geometric technic, namely powerful tool of algebraic cycles and motives. We also try to explain phenomena of relation between depth filtrations and moduli space of elliptic curves. Up to now, naive way of constructing Hodge realization of mixed Tate motives is still unclear. We also try to clarify conjectured construction by Bloch-Kriz. Moreover recently, we found a method to construct new algebraic cycles on abelian varieties, which seems to be useful to prove the algebraicity of Weil Hodge cycles.

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    • Motivic cohomology over discrete valuation rings

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      Geisser Thomas, Hesselholt Lars, Saito Shuji, Sato Kanetomo, Asakura Masanori

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      4 2011 - 3 2016

      Grant number：23340004

      Grant amount：\17680000 （ Direct Cost: \13600000 、 Indirect Cost：\4080000 ）

      Arithmetic geometry is the study of integral or rational solutions of systems of polynomial equations. For this, it is often useful to study the solutions in other domains, like complex number, real numbers, finite fields, or p-adic fields. An important invariant of such solution sets are motivic cohomology, higher Chow groups, and Suslin homology. During this project, I studied these invariants, and proved several interesting results about them.

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    • Non-commutative class field theory and Shimura varieties

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      FUJIWARA Kazuhiro, HESSELHOLT Lars, KATO Fumiharu, TAKAI Yuuki, GEISSER Thomas, KATO Fumiharu, KOBAYASHI Shinichi, KONDO Shigeyuki, SAITO Shuji, SAITO Takeshi

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      2009 - 2012

      Grant number：21340004

      Grant amount：\16380000 （ Direct Cost: \12600000 、 Indirect Cost：\3780000 ）

      Non-abelian class field theory is studied from various aspects, including a geometric viewpoint. As for foundations of rigid geometry, a joint research with F. Kato and O Gabber (IHES) went on based on international collaboration, yielding results on the Hausdorff completions of commutative rings. As a result of this research, the foundation of rigid geometry is now established in a more general framework,giving more flexibility in applications. We have also obtained a clear explanation of the relationships between the notion of R. Huber’s adic spaces and V. Berkovich’s Berkovich spaces.As part of non-abelian class field theory, we provide a new viewpointthat the deformation theory of Galois representations (Galois deformation theory) can be applied directly to number-theoretical problems. The author has studied the indivisibility of relative class numbers of quadratic extensions by a prime number p as a first example. This is established in general. Our collaborator Y. Takai gave a lower bound estimate for the number of such quadratic extensions, when the field is Galois over the rationals and p is sufficiently large.

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