2019/10/06 by Saurabh Gosavi, Gosavi, Saurabh
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1910.02473
openalex publication_date 2019/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be the function field of a curve over a complete discretely valued field. Let ℓ be a prime not equal to the characteristic of the residue field. Given a finite subgroup B in the ℓ torsion part of the Brauer group ℓBr(F), we define the index of B as the minimum of the degrees of field extensions which split all elements in B. In this manuscript, we give an upper bound for the index of any finite subgroup B in terms of arithmetic invariants of F. As a simple application of our result, given a quadratic form q/F, where F is the function field of a curve over an n-local field, we provide an upper bound to the minimum of degrees of field extensions L/F so that the Witt index of q⊗ L becomes the largest possible.