Asian Journal of Mathematics

Volume 19 (2015)

Number 1

On higher regulators of Siegel threefolds I: The vanishing on the boundary

Pages: 83 – 120



Francesco Lemma (Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France)


In this paper, we prove the vanishing of a map between the absolute Hodge cohomology spaces of the boundaries of the Baily-Borel compactifications of the product of two modular curves on one side and of the Siegel threefold on the other side. As an application, we construct some 1-extensions of mixed Hodge structures between the trivial Hodge structure and the middle-degree interior cohomology of the Siegel threefold, which come from motivic cohomology. These are conjecturally related to non-critical values of the degree $4$ $L$-function of some cuspidal automorphic representations of $\mathrm{GSp}_4$.


Siegel threefolds, higher regulators, mixed Hodge modules

2010 Mathematics Subject Classification

14D07, 19F27

Published 12 February 2015