2024/11/19 by David Loeffler, Sarah Livia Zerbes, Loeffler, David +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.1515/forum-2025-0062
Abstract In our earlier work with Christopher Skinner [D. Loeffler, C. Skinner and S. L. Zerbes, Euler systems for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>GSp</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mn>4</m:mn> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> GSp(4) , J. Eur. Math. Soc. (JEMS) 24 (2022), 2, 669–733], we constructed Euler systems for the 4-dimensional spin Galois representations corresponding to automorphic forms for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>GSp</m:mi> <m:mn>4</m:mn> </m:msub> </m:math> GSp4 . 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.