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arXiv · 2411.12576

A universal Euler system for GSp(4)

David Loeffler·Sarah Livia Zerbes
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Abstract

In our earlier work with Christopher Skinner (J. Eur. Math. Soc 24 (2022), no. 2; DOI 10.4171/JEMS/1124; Arxiv 1706.00201), we constructed Euler systems for the 4-dimensional spin Galois representations corresponding to automorphic forms for GSp(4). This construction depended on various arbitrary choices of local test data. In this paper, we use multiplicity-one results for smooth representations to determine how these Euler system classes depend on the choice of test data, showing that all of these classes lie in a 1-dimensional space and are explicit multiples (given by local zeta-integrals) of a "universal" class independent of the choice of test data.

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David Loeffler, Sarah Livia Zerbes. 2024-11-19. A universal Euler system for GSp(4). https://doi.org/10.1515/forum-2025-0062

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