p-part Bloch-Kato conjecture for Siegel modular forms of genus 2

Abstract: The Bloch-Kato conjecture relates the algebraic part of special $L$-values to the Selmer groups of the same motive. In this talk, we study the $p$-part of this conjecture for a Siegel modular form of genus $2$ and show, under mild conditions on the associated Galois representation, that the special value of the standard $L$-function divided by an automorphic period is equal to the characteristic ideal of the corresponding Selmer group, up to $p$-units. The proof relies on some non-vanishing results of mod $p$ theta lifts from the orthogonal group to the symplectic group.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper | slides )

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Rendez-vous on special values and periods

Series comments: The main objective of this conference is to gather together young researchers interested in special values of L-functions and periods. These objects are at the crossroads of many recent important developments in arithmetic geometry, such as Euler systems or the theory of motives. The different talks will portray the variety of viewpoints with which L-functions and periods are studied at present.

Registration is free and mandatory, to get access to the livestream and recording of the talks.

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