北大数論セミナー:G-displays over prisms and deformation theory(伊藤和広氏), Construction of quasi-canonical liftings of K3 surfaces of finite height in odd characteristic(井上絢太郎氏)

Event Date: Feb 20, 2023




Organizer:跡部 発、安田 正大



14:30-15:30 伊藤和広氏(東京大学カブリ数物連携宇宙研究機構)

Title:G-displays over prisms and deformation theory

The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups.
Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them. As an application, we give an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, using our deformation theory.

16:00-17:00 井上絢太郎氏(京都大学大学院理学研究科)

Title:Construction of quasi-canonical liftings of K3 surfaces of finite height in odd characteristic

Recently, Langer, Zink, and Lau introduced the notion of higher display and developed the display-theoretic deformation theory of K3 surfaces. In this talk, we study the display structure of the crystalline cohomology of deformations of a K3 surface of finite height in terms of the Dieudonné display of the enlarged formal Brauer group. As an application, we construct a quasi-canonical lifting of a K3 surface of finite height over a finite field of characteristic p ≥ 3. Such results are previously obtained by Nygaard-Ogus when p ≥ 5.