p-adic hyberbolicity for Shimura varieties.

Abstract: Let S be a complex Shimura variety and let S^bb be its Baily Borel compactification. Assuming that the level structure is torsion-free, Borel proved that any holomorphic map from a product of punctured discs to S extends to a map from a product of discs to S^bb. Consequently, every holomorphic map from a complex algebraic variety to S must actually be algebraic. I will discuss a p-adic analogue of this theorem. This is joint work with Oswal-Zhu-Patel in the setting of abelian Shimura varieties, and with Bakker-Oswal-Yao in the setting of non-abelian (exceptional) Shimura varieties.

algebraic geometrynumber theory

Audience: researchers in the topic

FGC-HRI-IPM Number Theory Webinars

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