A norm compatible system of Galois cohomology classes for $\mathrm{GSp}(4)$

Abstract

For a given de Rham p -adic Galois representation M , a conjecture of Perrin–Riou associates a p -adic L -function for M to a norm compatible system of Galois cohomology classes in the projective limit \varprojlim {}_n \mathrm{H}^1(ℚ(ζ_{p^n}), M) . We construct such a norm compatible system for the symplectic group \mathrm{G}\overleftarrow{\mathrm{Sp}}_4 . Our classes are cup-products of torsion sections of the large elliptic polylogarithm pro-sheaf; we rely on its norm compatibility and on some computations of weights in the cohomology of Siegel threefolds of our previous work.