Patching over fields

2007/10/08 by David Harbater, Harbater, David, Julia Hartmann +1 · 1 citation
Computer Science · Engineering · Mathematics · #12E30 #14H #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0710.1392

openalex publication_date 2007/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a new form of patching that is both far-reaching and more elementary than the previous versions that have been used in inverse Galois theory for function fields of curves. A key point of our approach is to work with fields and vector spaces, rather than rings and modules. After presenting a self-contained development of this form of patching, we obtain applications to other structures such as Brauer groups and differential modules.

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