Multiplicities of Representations in Algebraic Families
Number Theory
2024-02-21 v3 Representation Theory
Abstract
In this short notes, we consider multiplicities of representations in general algebraic families, especially the upper semi-continuity of homological multiplicities and the locally constancy of Euler-Poincare numbers. This generalizes the main result of Aizenbud-Sayag for unramified twisting families.
Keywords
Cite
@article{arxiv.2305.11557,
title = {Multiplicities of Representations in Algebraic Families},
author = {Li Cai and Yangyu Fan},
journal= {arXiv preprint arXiv:2305.11557},
year = {2024}
}
Comments
Part of the results overlaps with arXiv:2107.05921v1. To appear in Comptes Rendus-S\'erie Math\'ematique