Higher Hida theory and p-adic L-functions for GSp(4)

Abstract

We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of non-holomorphic automorphic forms for GSp(4), contributing to coherent cohomology of Siegel threefolds in positive degrees. We apply this new method to construct p-adic L-functions associated to the degree 4 (spin) L-function of automorphic representations of GSp(4), and the degree 8 L-function of GSp(4) x GL(2).

Final version, now published in "Duke Math Journal"

References in corpus (4)

• An Euler system for GU(2, 1)
• Coherent cohomology of Shimura varieties and automorphic forms
• Hecke operators and the coherent cohomology of Shimura varieties
• Special L-values and Selmer groups of Siegel modular forms of genus 2

Cited by in corpus (15)

• On the Bloch-Kato conjecture for GSp(4)
• An Euler system for GU(2, 1)
• P-adic L-functions and diagonal cycles for GSp(4) x GL(2) x GL(2)
• On local zeta-integrals for GSp(4) and GSp(4) x GL(2)
• On some zeta-integrals for unramified representations of GSp(4)
• On the Bloch--Kato conjecture for GSp(4) x GL(2)
• On p-adic regulators for GSp(4) x GL(2) and GSp(4) x GL(2) x GL(2)
• On the Bloch--Kato conjecture for the symmetric cube
• Iwasawa theory for quadratic Hilbert modular forms
• On the p-adic interpolation of unitary Friedberg--Jacquet periods
• An introduction to Eisenstein measures
• Higher Hida theory for Hilbert modular varieties in the totally split case
• P-adic L-functions for GL(3)
• Special cycles on orthogonal Shimura varieties
• On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces