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: https://umich.zoom.us/j/99042229905 Speaker(s): Haoyang Guo (UM)