Spinor class fields for sheaves of lattices

TL;DR

This paper extends the theory of spinor class fields and representation fields from lattices over number fields to sheaves of lattices over algebraic curves over finite fields, broadening its mathematical scope.

Contribution

It introduces a generalization of spinor class field theory to sheaves of lattices on algebraic curves over finite fields, expanding the classical framework.

Findings

Generalization of spinor class field theory to sheaves of lattices

Application to lattices over coordinate rings of algebraic curves

Framework for further research in algebraic geometry and number theory

Abstract

We extend the theory of spinor class field and representation fields previously defined for lattices over the ring of integers of a number field to both, lattices over the coordinate ring of a smooth irreducible affine curve over a finite field, and sheaves of lattices over the structure sheaf of an irreducible smooth projective curve over a finite field.