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

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

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

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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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