On the supersingular reduction of K3 surfaces with complex multiplication

Date: 
2017/12/22 Fri 10:30 - 12:00
Room: 
Room 152, Building No.3
Speaker: 
伊藤和広
Affiliation: 
京都大学
Abstract: 

As an analogue of the theory of complex multiplication (CM) for abelian varieties, Rizov proved the main theorem of CM for K3 surfaces. In this talk, we will study the good reduction modulo p of K3 surfaces with CM. We will determine when the good reduction is supersingular. Moreover, for almost all p, we will calculate its Artin invariant. The proof relies on the main theorem of CM for K3 surfaces and the integral p-adic Hodge theory recently established by Bhatt, Morrow, and Scholze. Our results generalize Shimada's results on complex projective K3 surfaces with Picard number 20.