English

Coherent cohomology of Shimura varieties and automorphic forms

Number Theory 2024-07-31 v2 Algebraic Geometry

Abstract

We show that the cohomology of canonical extensions of automorphic vector bundles over toroidal compactifications of Shimura varieties can be computed by relative Lie algebra cohomology of automorphic forms. Our result is inspired by and parallel to Borel and Franke's work on the cohomology of automorphic local systems on locally symmetric spaces, and also generalizes a theorem of Mumford.

Keywords

Cite

@article{arxiv.1810.12056,
  title  = {Coherent cohomology of Shimura varieties and automorphic forms},
  author = {Jun Su},
  journal= {arXiv preprint arXiv:1810.12056},
  year   = {2024}
}

Comments

Slightly revised. Appeared in the journal in a different typesetting