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arXiv · 1807.06512

Norm-compatible systems of Galois cohomology classes for $GSp_6$

Antonio Cauchi·Joaquín Rodrigues Jacinto
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Abstract

We construct global cohomology classes in the middle degree cohomology 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 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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Antonio Cauchi, Joaquín Rodrigues Jacinto. 2018-07-17. Norm-compatible systems of Galois cohomology classes for $GSp_6$. https://arxiv.org/abs/1807.06512

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