IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Galois cohomology and forms of algebras over Laurent polynomial rings
Autor/es:
P. GILLE AND A. PIANZOLA
Revista:
MATHEMATISCHE ANNALEN
Referencias:
Año: 2007 vol. 338 p. 497 - 497
ISSN:
0025-5831
Resumen:
The main thrust of this work is the study of two seemingly unrelated questions: Non-abelian Galois cohomology of Laurent polynomial rings on the one hand, while on the other,  a class of infinite dimensional Lie algebras which, as rough approximations, can be thought off as higher nullity analogues of the affine Kac-Moody Lie algebras. Though the algebras in question are in general infinite dimensional over the given base field (say the complex numbers), they can be thought as being finite  provided that the base field is now replaced by  the centroid of the algebras, (which turns out to be a Laurent polynomial ring). This leads us to the theory of reductive group schemes as developed by M. Demazure and A. Grothendieck. Once this point of view is taken, Algebraic Principal Homogeneous Spaces (torsors) and their accompanying non-abelian \'etale cohomology, arise naturally.