WEEKLY ACTIVITIES

Thời gian: 16h30, thứ năm, 02/05/2024

Hình thức: Offline tại phòng 612 nhà A6 hoặc online qua google meet, link cụ thể https://meet.google.com/yep-kbzk-eao?pli=1&authuser=1

Tóm tắt: Fix a prime number p. Let K be a finite extension of Qp and let G denote the absolute Galois group of K, with I as its inertial subgroup. Now, let A be an Abelian variety defined over K. Grothendieck's celebrated theorem states that for a prime number l different from p, A has semi-stable reduction if and only if the action of I on the ell-adic Tate module T_ell(A) is unipotent.

In this talk, we delve into the scenario where ell = p. Using p-adic Hodge theory, we investigate the Galois action of both G and I on the p-adic Tate module T_p(A). Surprisingly, it often emerges that the invariant T_p(A)^{I_K} = 0 when A possesses semi-stable reduction.