TY - CHAP
T1 - Field patching, factorization, and local-global principles
AU - Krashen, Daniel
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
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U2 - 10.1007/978-1-4419-6211-9_4
DO - 10.1007/978-1-4419-6211-9_4
M3 - Chapter
AN - SCOPUS:84859517065
SN - 9781441962102
T3 - Developments in Mathematics
SP - 57
EP - 82
BT - QUADRATIC FORMS, LINEAR ALGEBRAIC GROUPS, AND COHOMOLOGY
A2 - COLLIOT-THELENE, JEAN-LOUIS
A2 - GARIBALDI, SKIP
A2 - SUJATHA, R.
A2 - SURESH, VENAPALLY
ER -