Patching
The term patching describes the process of building a global object from certain
local pieces. It is a method that has been used to prove results in Galois
theory (e.g., for the solution of inverse problems and embedding
problems). There are several versions of patching in the literature, such as
formal, rigid, and algebraic patching. In a project with David Harbater , we introduce a new
version of patching over fields, which is more elementary formal or rigid
patching, but more general than algebraic patching. There are various
applications of this, including differential modules (e.g., inverse problems and
embedding problems in
differential Galois theory) and division algebras (together with Daniel Krashen ).
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