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

Francesco Lemma; Tadashi Ochiai

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arXiv · 2504.18304

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

Francesco Lemma·Tadashi Ochiai

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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 $(3,3)$.

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Francesco Lemma, Tadashi Ochiai. 2025-04-25. Kato explicit reciprocity law for Siegel modular forms of weight $(3, 3)$. https://arxiv.org/abs/2504.18304

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