Abstract:

The lecture series will focus on the results and techniques used in the first part (§1) of Kisin’s work on integral models for Shimura varieties of abelian type[Kisin, 2010]. We will discuss Breuil-Kisin classifications of crystalline representations studied in [Kisin, 2006], with its applications to the classification of pdivisible groups. We will also cover some relative integral  $p$-adic Hodge theory after Faltings with its applications to the deformations theory of  $p$-divisible groups as in [Faltings, 1999] and [Faltings, 1988]. If time permits, we will also bring together some recent points of view on the above results, and discuss the above results for  $p$-divisible groups with $\mathcal{G}$-structures, with $\mathcal{G}$ certain reductive group scheme over $\mathbb{Z}_p$ as in [Kisin, 2010].

References:

[Faltings, 1988] Faltings, G. (1988). Crystalline cohomology and p-adic Galois representations. In Algebraic analysis, geometry, and number theory, pages 25–80, Baltimore. The Johns Hopkins University Press.
[Faltings, 1999] Faltings, G. (1999). Integral crystalline cohomology over very ramified valuation rings. J. Am. Math. Soc., 12(1):117–144. 

[Kisin, 2006] Kisin, M. (2006). Crystalline representations and F-crystals. In Algebraic geometry and number theory, volume 253 of Progr. Math., pages 459–496, Boston. Birkh¨auser.
[Kisin, 2010] Kisin, M. (2010). Integral models for Shimura varieties of abelian type. J. Am. Math. Soc., 23(4):967–1012.
 

Time:

5.18 、5.19 、5.25 、5.26       1：30pm—3：00pm