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Researcher List >> Trihan Fabien Benoit
 

Trihan Fabien Benoit

 
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NameTrihan Fabien Benoit
Alternative NamesTrihan Fabien
AffiliationSophia University
SectionFaculty of Science and Technology, Department of Information and Communication Sciences
Job titleAssociate Professor
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)
Research funding number60738300
J-Global ID201401054300838945

Profile

(Subject of research)
Geometric Iwasawa Theory

Research Interests

 
Number Theory

Research Areas

 
  • Natural sciences / Algebra / 

Papers

 
 
King Fai Lai   Ignazio Longhi   Takashi Suzuki   Ki Seng Tan   Fabien Trihan   
Algebra and Number Theory   15(4) 863-907   2021
Let A be an abelian variety over a global function field K of characteristic p. We study the µ-invariant appearing in the Iwasawa theory of A over the unramified ℤp-extension of K. Ulmer suggests that this invariant is equal to what he calls the d...
 
Fabien Trihan   David Vauclair   
Proceedings of the American Mathematical Society   149(9) 3601-3611   2021
We state and prove certain cases of the equivariant Tamagawa number conjecture of a semistable Abelian variety over an everywhere unramified finite Galois extension of a global field of characteristic p > 0 under a semisimplicity hypothesis.
 
Trihan Fabien   Vauclair   David   
Documenta mathematica   24 473-522   2019   [Refereed]
We establish the Iwasawa main onje ture for semistable abelian varieties over a function field of charateristi p under certain restrictive assumptions. Namely we consider p-torsion free p-adic Lie extensions of the base field which contain the con...
 
King Fai Lai   Ignazio Longhi   Ki-Seng Tan   Fabien Trihan   
Transactions of the American Mathematical Society   370(3) 1925-1958   2018   [Refereed]
We prove a functional equation for two projective systems of finite abelian p-groups, {an} and {abn}, endowed with an action of ℤdp such that an can be identified with the Pontryagin dual of bn for all n. Let K be a global field. Let L be a ℤdp-ex...
 
King Fai Lai   Ignazio Longhi   Ki-Seng Tan   Fabien Trihan   
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY   112(6) 1040-1058   Jun 2016   
We study a geometric analogue of the Iwasawa Main Conjecture for constant ordinary abelian varieties over Z(p)(d)-extensions of function fields ramifying at a finite set of places.

Books and Other Publications

 
 
Trihan Fabien Benoit(Part:Joint edit, p.1-337)
Birkhäuser , Springer   4 Dec 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 arithme...
 
Trihan Fabien Benoit(Part:Joint author, p.119-181)
Birkhäuser , Springer   4 Dec 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

 
 
Class number formula over global field of characteristic p and with coefficients.
日本学術振興会: 科学研究費助成事業
TRIHAN FABIEN 
Project Year: Apr 2021 - Mar 2026
 
Geometric Iwasawa Theory
Japan Society for the Promotion of Science: Grants-in-Aid for Scientific Research
TRIHAN FABIEN 
Project Year: Apr 2015 - Mar 2019