p-adic Siegel disks on K3 surfaces

Abstract: McMullen constructed interesting automorphisms of complex K3 surfaces that have positive entropy, hence act chaotically on a large set, yet have a region of well-behaved orbits where the action is equivalent to a rotation. This region is called a Siegel disk. Strikingly, a K3 with such an automorphism is necessarily non-projective, its properties accessible only through the Torelli theorem.

In this talk, we will build a p-adic analog of McMullen's living on a non-projective p-adic analytic K3 surface. We can synthesize this surface without appealing to the Torelli theorem, making the construction more flexible.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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