Patching over fields
David Harbater (U. Pennsylvania), Julia Hartmann (U. Heidelberg)

TL;DR
This paper introduces a new, more elementary patching method for fields and vector spaces, expanding its applications in inverse Galois theory, Brauer groups, and differential modules.
Contribution
It develops a novel patching approach based on fields and vector spaces, simplifying previous methods and broadening their applicability.
Findings
New patching method applicable to fields and vector spaces
Applications to inverse Galois theory for function fields
Extensions to Brauer groups and differential modules
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques · Polynomial and algebraic computation
