Multiplicities of Representations in Algebraic Families

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.

Part of the results overlaps with arXiv:2107.05921v1. To appear in Comptes Rendus-Série Mathématique