研究者業績
基本情報
- 所属
- 上智大学 理工学部情報理工学科 准教授
- 学位
- 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)
- 通称等の別名
- Trihan Fabien
- 研究者番号
- 60738300
- J-GLOBAL ID
- 201401054300838945
- researchmap会員ID
- 7000007568
(Subject of research)
Geometric Iwasawa Theory
研究キーワード
1研究分野
1論文
25-
Research in the Mathematical Sciences 12(4) 2025年9月11日 査読有り
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Comptes Rendus. Mathématique 363(G9) 867-871 2025年7月15日 査読有り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.
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Memoirs of the American Mathematical Society 299(1495) 2024年7月 査読有り<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>
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Algebra and Number Theory 15(4) 863-907 2021年 査読有り
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Proceedings of the American Mathematical Society 149(9) 3601-3611 2021年 査読有り
書籍等出版物
2-
Birkhäuser , Springer 2014年12月4日 (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.
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Birkhäuser , Springer 2014年12月4日 (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
共同研究・競争的資金等の研究課題
2-
日本学術振興会 科学研究費助成事業 2021年4月 - 2026年3月
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日本学術振興会 科学研究費助成事業 2015年4月 - 2019年3月