Field Patching, Factorization, and Local–Global Principles

Part of the Developments in Mathematics book series (DEVM, volume 18)


The method of field patching has proven useful in obtaining results on Galois theory, central simple algebras, and quadratic forms. A crucial ingredient for this was proving certain “factorization” results for connected, rational linear algebraic groups. In this paper, we explore other possible applications of field patching by examining the relationship between factorization results and local–global principles, and also by extending the known factorization results to connected, retract rational linear algebraic groups.


Quadratic Form Algebraic Group Monoidal Category Linear Algebraic Group Central Simple Algebra 
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© Springer New York 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

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