The Clifford algebra of a finite morphism

TL;DR

This paper develops a comprehensive theory of Clifford algebras associated with finite morphisms of schemes, with applications to Ulrich bundles and period-index problems for genus 1 curves.

Contribution

It introduces a new framework for Clifford algebras in algebraic geometry, linking finite morphisms to vector bundle theory and arithmetic problems.

Findings

Established a general construction of Clifford algebras for finite scheme morphisms

Connected Clifford algebra theory to Ulrich bundle classification

Applied results to period-index problems for genus 1 curves

Abstract

We develop a general theory of Clifford algebras for finite morphisms of schemes and describe applications to the theory of Ulrich bundles and connections to period-index problems for curves of genus 1.