Polylogarithms for GL₂ over totally real fields

2016/04/14 by Graf, Philipp
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1604.04209

Abstract

We give a new, purely topological construction of Eisenstein cohomology classes for Hilbert-Blumenthal varieties using the polylogarithm for families of topological tori and a decomposition with respect to the units in the center of GL₂. These classes are explicitly calculated in de Rham chomology and compared with Harder's Eisenstein classes. For non-trivial coefficient systems the whole Eisenstein cohomology in positive degrees is generated by these topological Eisenstein classes. This gives an alternative proof for the rationality of Harder's Eisenstein operator without using any multiplicity one arguments. The text constitutes my 2016 Regensburg PhD thesis.

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