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Algebraic Geometry Seminar
Seminar information archive ～05/07｜Next seminar｜Future seminars 05/08～
| Date, time & place | Friday 13:30 - 15:00 118Room #118 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, KAWAKAMI Tatsuro, ENOKIZONO Makoto |
2026/05/12
13:30-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shuji Saito (University of Tokyo)
Birational lattices in the cohomology of the structure sheaf over non-archimedean fields
Shuji Saito (University of Tokyo)
Birational lattices in the cohomology of the structure sheaf over non-archimedean fields
[ Abstract ]
We show that the cohomology of the structure sheaf of smooth and proper varieties over a complete non-archimedean field K with the ring R of integers of characteristic zero, can be refined to a birational cohomology theory of smooth (not necessarily proper) varieties over K with values in R-lattices, and the same holds for K of positive characteristic in dimensions at most 3.
As one application, we obtain that the automorphism group of the function field of a proper smooth variety X of dimension at most 3 over any field of positive characteristic acts quasi-unipotently on the cohomology of the canonical sheaf of X. The proof relies on some results from rigid analytic geometry on the cohomology of twisted integral rigid structure sheaves due to Bartenwerfer and van der Put.
This is a joint work with A. Merici and Kay Ruelling.
We show that the cohomology of the structure sheaf of smooth and proper varieties over a complete non-archimedean field K with the ring R of integers of characteristic zero, can be refined to a birational cohomology theory of smooth (not necessarily proper) varieties over K with values in R-lattices, and the same holds for K of positive characteristic in dimensions at most 3.
As one application, we obtain that the automorphism group of the function field of a proper smooth variety X of dimension at most 3 over any field of positive characteristic acts quasi-unipotently on the cohomology of the canonical sheaf of X. The proof relies on some results from rigid analytic geometry on the cohomology of twisted integral rigid structure sheaves due to Bartenwerfer and van der Put.
This is a joint work with A. Merici and Kay Ruelling.
