A prismatic Herr complex for Bloch–Kato Selmer groups

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu, Huajie Li

Speaker：

Luming Zhao (Dalian University of Technology)

Time：

Monday, 10:00- 11:00 am, Dec. 22, 2025

Venue：

B627, Shuangqing Complex Building A

Title:

A prismatic Herr complex for Bloch–Kato Selmer groups

Abstract:

In 1998, Laurent Herr constructed a three-term complex using étale (phi, Gamma)-modules to compute the Galois cohomology of corresponding Galois representations. This approach was later extended to various settings, and recently to Kummer setting via (phi, tau)-modules.

Inspired by the work of Du–Liu, we will introduce a prismatic Herr complex, formulated using a prismatic version of (phi, tau)-modules attached to a (log-)crystalline representation. For a crystalline representation, this complex computes the Bloch–Kato Selmer group and relates to the cohomology of the corresponding F-gauge. The talk is based on joint work with Heng Du.