Corank spectral sequence for locally symmetric varieties
Algebraic Geometry
2025-03-04 v2 Algebraic Topology
Number Theory
Abstract
We construct a new type of spectral sequences for the mixed Hodge structures on the cohomology of locally symmetric varieties. These spectral sequences converge to the edge components in the Hodge triangles, and the E1-terms are expressed by group cohomology associated to the cusps. They already degenerate at E1 in a certain range, which gives a simple expression of some Hodge components. An identity of holomorphic Euler numbers is obtained as a consequence.
Cite
@article{arxiv.2401.07693,
title = {Corank spectral sequence for locally symmetric varieties},
author = {Shouhei Ma},
journal= {arXiv preprint arXiv:2401.07693},
year = {2025}
}
Comments
An error concerning monodromy action on the toroidal boundary strata was corrected. Accordingly, the paper was largely rewritten. The previous section on the Borel-Serre boundary was dropped for restricting the focus and the page length; this will be taken up on another occasion