Perfectoid covers of abelian varieties and the weight-monodromy conjecture

Abstract: Deligne's weight-monodromy conjecture gives control over the zeros of local factors of L-functions of varieties at places of bad reduction. His proof in characteristic p was a step in his proof of the generalized Weil conjectures. Scholze developed the theory of perfectoid spaces to transfer Deligne's proof to characteristic 0, proving the conjecture for complete intersections in toric varieties. Building on Scholze's techniques, we prove the weight-monodromy conjecture for complete intersections in abelian varieties. Part of this talk will discuss joint work with Blakestad, Gvirtz, Heuer, Shchedrina, Shimizu, and Yao.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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