Special cycles on simple Shimura varieties

Abstract: This is a work in progress inspired by the the arithmetic Gan--Gross--Prasad conjecture where one is interested in the arithmetic diagonal cycle on the product of two Shimura varieties. We study special cycles on simple Shimura varieties attached to central
simple algebras with an involution of second kind. We study some local questions arising from the relative trace formula approach.

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Affiliation

Massachusetts Institute of Technology

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