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Department of Mathematics,
University of California San Diego

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Final Defense

Peter Wear

UCSD

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.

Advisor: Kiran Kedlaya

May 29, 2020

10:00 AM

Contact Peter Wear for Zoom link

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