Norm-compatible systems of Galois cohomology classes for GSp₆

2018/07/17 by Antonio Cauchi, Cauchi, Antonio, Joaquín Rodrigues Jacinto +1
Arts and Humanities · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1807.06512

openalex publication_date 2018/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct global cohomology classes in the middle degree cohomology of the Shimura variety of the symplectic group GSp₆ compatible when one varies the level at p. These classes are expected constituents of an Euler system for the Galois representations appearing in these cohomology groups. As an application, we show how these classes provide elements in the Iwasawa cohomology of these representations and, by applying Perrin-Riou's machinery, p-adic L-functions associated to them.

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