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日仏数学拠点FJ-LMIセミナー
過去の記録 ～05/01｜次回の予定｜今後の予定 05/02～
| 担当者 | 小林俊行, ミカエル ペブズナー |
|---|
2024年10月02日(水)
13:30-14:30 数理科学研究科棟(駒場) 122号室
Daniel CARO 氏 (Université de Caen Normandie)
Introduction to arithmetic D-modules (英語)
https://fj-lmi.cnrs.fr/seminars/
Daniel CARO 氏 (Université de Caen Normandie)
Introduction to arithmetic D-modules (英語)
[ 講演概要 ]
In this talk, I will give a brief overview of the theory of D-arithmetic modules, initiated by P. Berthelot in the 90's. By replacing the analytic or complex algebraic varieties by algebraic varieties defined over a field of characteristic p>0, this corresponds to an arithmetic analogue of the usual theory of D-modules. This makes it possible to obtain categories of p-adic objects associated with varieties of characteristic p; these p-adic coefficients satisfying a six functors formalism as expected. Via the de Rham cohomology associated with the constant arithmetic D-module, we obtain a p-adic interpretation and the rationality of the Weil zeta function, an arithmetic avatar of the Riemann zeta function, as well as a p-adic analogue of the Riemann hypothesis.
[ 講演参考URL ]In this talk, I will give a brief overview of the theory of D-arithmetic modules, initiated by P. Berthelot in the 90's. By replacing the analytic or complex algebraic varieties by algebraic varieties defined over a field of characteristic p>0, this corresponds to an arithmetic analogue of the usual theory of D-modules. This makes it possible to obtain categories of p-adic objects associated with varieties of characteristic p; these p-adic coefficients satisfying a six functors formalism as expected. Via the de Rham cohomology associated with the constant arithmetic D-module, we obtain a p-adic interpretation and the rationality of the Weil zeta function, an arithmetic avatar of the Riemann zeta function, as well as a p-adic analogue of the Riemann hypothesis.
https://fj-lmi.cnrs.fr/seminars/
