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  2. Trihan Fabien Benoit

Trihan Fabien Benoit

  (BENOIT TRIHAN FABIEN)

Profile Information

Affiliation
Associate Professor, Faculty of Science and Technology, Department of Information and Communication Sciences, Sophia University
Degree
学士(レンヌ第一大学)
修士(レンヌ第一大学)
DEA(レンヌ第一大学)
Ph.D(University of Rennes 1)
博士（純粋数学）(レンヌ第一大学)
Other name(s) (e.g. nickname)
Trihan Fabien
Researcher number
60738300
J-GLOBAL ID
201401054300838945
researchmap Member ID
7000007568

(Subject of research)
Geometric Iwasawa Theory

Research Interests

 1

Research Areas

 1

Papers

 25
  • Ki-Seng Tan, Fabien Trihan, Kwok-Wing Tsoi
    Research in the Mathematical Sciences, 12(4), Sep 11, 2025  Peer-reviewed
  • Bruno Chiarellotto, Fabien Trihan
    Comptes Rendus. Mathématique, 363(G9) 867-871, Jul 15, 2025  Peer-reviewed
    In this paper, we apply Tsuzuki’s main theorem in [12] to establish a criterion for when two abelian varieties over a function field of characteristic are isogenous. Specifically, assuming that their endomorphism algebras tensored with are division algebras, we prove that if the maximal quotients of minimal slope (i.e., the unique maximal isoclinic quotient corresponding to the minimal slope, defined up to isogeny) of their associated -divisible groups are isogenous, then the abelian varieties themselves are isogenous over . We also extend this result to certain -divisible groups, highlighting the deep connection between isogenies of abelian varieties and the structure of overconvergent -isocrystals.
  • Fabien Trihan, David Vauclair
    Memoirs of the American Mathematical Society, 299(1495), Jul, 2024  Peer-reviewed
    <p>We compare flat cohomology to crystalline syntomic complexes with coefficients in two cases: (1) -divisible groups over a separated -scheme with local finite -bases, (2) semi-abelian schemes over a separated irreducible smooth curve.</p>
  • King Fai Lai, Ignazio Longhi, Takashi Suzuki, Ki Seng Tan, Fabien Trihan
    Algebra and Number Theory, 15(4) 863-907, 2021  Peer-reviewed
  • Fabien Trihan, David Vauclair
    Proceedings of the American Mathematical Society, 149(9) 3601-3611, 2021  Peer-reviewed
More

Books and Other Publications

 2
  • Trihan Fabien Benoit (Role: Joint editor, p.1-337)
    Birkhäuser , Springer, Dec 4, 2014 (ISBN: 9783034808521)
    This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields.
  • Trihan Fabien Benoit (Role: Joint author, p.119-181)
    Birkhäuser , Springer, Dec 4, 2014 (ISBN: 9783034808521)
    We give a proof of the Iwasawa Main Conjecture for smooth Zp-sheaves (resp. semistable abelian varieties) over (resp. unramified) p-adic Lie extensions of function fields

Research Projects

 2

Other

 1
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