Patching over fields

By D. Harbater, Julia Hartmann. 2007

69 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a0616b5beb1d8cb03bba7b84f8cf258acf4ae56e

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Patching and local-global principles for homogeneous spaces over function fields of p-adic curves (2008, background): “Let us recall basic notation from [14] and [15].”
Applications of patching to quadratic forms and central simple algebras (2008, methodology): “The above decomposition theorem will be used in the next section to extend [ HH07 ], Proposition 3.2, which used an additive decomposition to provide a factorization of matrices in GLn.”