Hermitian and skew hermitian forms over local rings

摘要

We investigate the structure of possibly degenerate epsilon-hermitian forms over local rings. We prove classification theorems in the cases where the ring is complete and either the form is nondegenerate or the ring is a discrete valuation ring. In the latter case we describe a complete set of invariants for such forms based on a generalisation of the classical notion of the radical of the form. (C) 2018 Elsevier Inc. All rights reserved.