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Special Events Seminar

Dissertation Defense: Cohomology of non-smooth rigid analytic spaces
Friday, May 7, 2021
2:00-4:00 PM
Off Campus Location
This thesis considers the cohomology theories of rigid analytic spaces, with a focus on spaces that might be singular. Analogous to the complex algebraic geometry, we generalize derived de Rham cohomology, infinitesimal cohomology, and Deligne--Du Bois cohomology to their rigid analytic counterparts, and study their relations. We also consider the p-adic \'etale cohomology of rigid analytic spaces, extending the Hodge--Tate decomposition theorem of Faltings and Scholze to non-smooth rigid analytic spaces. The strategy to the latter is the simplicial method and the resolution of singularities. Furthermore, joint with Shizhang Li, we reproduce the period sheaves and the p-adic Poincar\'e sequence in p-adic Hodge theory, using the derived de Rham complex.

Haoyang's advisor is Bhargav Bhatt.

Zoom: Speaker(s): Haoyang Guo (UM)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics