Title: On the cohomology groups of local systems over hilbert modular varieties

Speaker: Prof. Ye Xuanming, Sun Yat-Sen University

Time: 10:10-12:00 am, April 18th(Thursday), 2013

Abstract. Let X be a Hilbert modular variety and V a non-trivial local system over X with infinite monodromy. We study Saito’s mixed Hodge structure (MHS) on the cohomology groups H^k(X,V) using the method of Higgs bundles. Among other results we prove the Eicher-Shimura isomorphism, give a dimension formula for the Hodge numbers. These results are analogous to [1] in the cocompact case and complement the results in [2] for constant coefficients.

[1] Matsushima, Y., Shimura, G., On the cohomology groups attached to certain vector valued differential forms on the product of the upper half planes, Ann. of Math., 78, 417-449, 1963.

[2] Freitag, E., Hilbert modular forms, Springer-Verlag, Berlin, 1990.