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Gan-Gross-Prasad Cycles and Derivatives of P-Adic L-Functions

Shimura Varieties and L-Functions March 13, 2023 - March 17, 2023

March 17, 2023 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Daniel Disegni (Ben Gurion University of the Negev)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Gan-Gross-Prasad Cycles And Derivatives Of P-Adic L-Functions

Abstract

Certain Rankin-Selberg motives of rank n(n+1) are endowed with algebraic cycles arising from maps of unitary Shimura varieties. Gan-Gross-Prasad conjectured that these cycles are analogous to Heegner points, in the sense that their nontriviality should be detected by derivatives of L-functions.

I will propose another nontriviality criterion, based on p-adic L-functions. Under some assumptions, this variant can be established in a refined quantitative form, via a comparison of p-adic relative-trace formulas. Together with the recent LTXZZ Euler system, this gives cases of the p-adic Beilinson-Bloch-Kato conjecture of Perrin-Riou. (Joint work with Wei Zhang.)

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Gan-Gross-Prasad Cycles And Derivatives Of P-Adic L-Functions

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