Kato explicit reciprocity law for Siegel modular forms of weight (3, 3)

2025/04/25 by Lemma, Francesco, Ochiai, Tadashi
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.18304

Abstract

We extend Kato explicit reciprocity law, in the version written by Scholl, for a modular curve to a product of two modular curves. By embedding the product of two modular curves in the Siegel threefold, we deduce an explicit reciprocity law for the unique critical twist of the p-adic Galois representation attached to cuspidal Siegel modular forms of weight (3,3).

Related

• On the Bloch-Kato conjecture for GSp(4)
• An explicit version of Shimura's reciprocity law for Siegel modular\n functions
• CHL Calabi-Yau threefolds: Curve counting, Mathieu moonshine and Siegel modular forms
• On the p-adic integration over Igusa towers of Siegel modular varieties
• Arithmetic level raising on triple product of Shimura curves and Gross--Kudla--Schoen Diagonal cycles II: Bipartite Euler system