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Group, Lie and Number Theory Seminar

Irrational periods of Hilbert Eisenstein series
Monday, January 14, 2019
4:00-5:20 PM
4088 East Hall Map
Unlike the Eisenstein series E_k for k > 2, the Eisenstein series E_2 for SL_2(Z) is not holomorphic. In this talk, we will describe an analogous phenomenon for Eisenstein series on Hilbert modular varieties. We will show that the periods of the holomorphic Eisenstein series of level 1, parallel weight 2, on a Hilbert modular surface are not rational, even up to scaling. Similar results hold for Hilbert modular varieties of all dimensions, and for extensions of Galois representations occuring in étale cohomology. For the étale results, the key point is to study the restriction of the canonical extension of the Hodge bundle to the boundary of a smooth toroidal compactification. Speaker(s): Jesse Silliman (Stanford)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics