Commentarii Mathematici Helvetici


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Volume 85, Issue 4, 2010, pp. 885–905
DOI: 10.4171/CMH/213

Published online: 2010-08-31

A norm compatible system of Galois cohomology classes for GSp(4)

Francesco Lemma[1]

(1) Villaz, France

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 limnH1(ℚ(ζpn), M). We construct such a norm compatible system for the symplectic group GSp4. 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.

Keywords: Elliptic polylogarithm pro-sheaf, p-adic L-function, Siegel modular variety

Lemma Francesco: A norm compatible system of Galois cohomology classes for GSp(4). Comment. Math. Helv. 85 (2010), 885-905. doi: 10.4171/CMH/213