Norm-Compatible Systems of Galois Cohomology Classes for $\mathbf{GSp}_6$

Antonio Cauchi; Joaquín Rodrigues Jacinto

doi:10.4171/dm/767

JournalsdmVol. 25pp. 911–954

Norm-Compatible Systems of Galois Cohomology Classes for $GSp_{6}$

Antonio Cauchi
Departament de Matemátiques, Universitat Politécnica de Catalunya, Edifici Omega, Despatx 419, C. Jordi Girona 1-3, 08034 Barcelona, Spain
Joaquín Rodrigues Jacinto
Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, 46 allée d'Italie 69, 364 Lyon Cedex 07, France

$Norm-Compatible Systems of Galois Cohomology Classes for $\mathbf{GSp}_6$ cover$

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Abstract

We construct global cohomology classes in the middle degree plus one cohomology group of the Shimura variety of the symplectic group $GSp_{6}$ compatible when one varies the level at $p$ . These classes are expected constituents of an Euler system for the Galois representations appearing in the middle degree étale cohomology groups of the aforementioned variety. 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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Antonio Cauchi, Joaquín Rodrigues Jacinto, Norm-Compatible Systems of Galois Cohomology Classes for $GSp_{6}$ . Doc. Math. 25 (2020), pp. 911–954

DOI 10.4171/DM/767