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BIMSA-YMSC Tsinghua Number Theory Seminar
A prismatic Herr complex for Bloch–Kato Selmer groups
A prismatic Herr complex for Bloch–Kato Selmer groups
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Luming Zhao
Time
Monday, December 22, 2025 10:00 AM - 11:00 AM
Venue
Shuangqing-B627
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.