Algebra seminar
Pavel Čoupek (Michigan State Univ.): Ramification bounds via Breuil-Kisin and q-crystalline cohomology
Abstract: Let K be a finite extension of Q_p of ramification index e., and let X be a smooth proper scheme over the ring of integers of K. I will discuss how to obtain bounds on ramification for the mod p Galois representation arising from i-th étale cohomology of (geometric generic fiber of) X in terms of i, p and e. Key input in achieving this are various instances of prismatic cohomology of X: in general, one can use the Breuil-Kisin cohomology together with the Ainf-cohomology of X, and a series of conditions that control the Galois action on elements of the former inside the latter. When K/Q_p is unramified, one can similarly use q-crystalline cohomology to obtain slightly better bounds. (This last part is current work in progress.
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.
