Year: 2025
Type: article
Abstract: We prove Pfister’s local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is 2 -primary torsion. Our proof relies on a hermitian version of Sylvester’s law of inertia, which is obtained from an investigation of the connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms.
Source: Documenta Mathematica
DOI: 10.4171/dm/1026
Authors: Vincent Astier, Thomas Unger
Institution: University College Dublin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Fondazione Bruno Kessler
OpenAlex ID: W4413833843