Rank one Eisenstein cohomology of local systems on the moduli space of abelian varieties

TL;DR

This paper derives formulas for Eisenstein cohomology of local systems on the moduli space of abelian varieties, including explicit results for genus 2, advancing understanding of their cohomological structure.

Contribution

It provides explicit formulas for Eisenstein cohomology in the context of abelian varieties, particularly for rank 1 degenerations and genus 2 cases.

Findings

Formula for Eisenstein cohomology on partial compactification

Explicit Eisenstein cohomology formula for genus 2

Enhanced understanding of cohomological structure of moduli spaces

Abstract

We give a formula for the Eisenstein cohomology of local systems on the partial compactification of the moduli of principally polarized abelian varieties given by rank 1 degenerations. For genus 2 we give a formula for the full Eisenstein cohomology.