A universal Euler system for GSp 4

Abstract In our earlier work with Christopher Skinner [D. Loeffler, C. Skinner and S. L. Zerbes, Euler systems for GSp ⁢ ( 4 ) \mathrm{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 GSp 4 \mathrm{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.