Noncommutataive Descent and Non-Abelian Cohomology

Nuss, Philippe

Institut de Recherche Mathématique Avancée, Université Louis-Pasteur et CNRS, 7, rue René-Descartes, 67084 Strasbourg Cedex, France. e-mail: [email protected]

K-Theory 12(1):p 23-74, July 1997.

We study the descent problem of modules over general extensions of noncommutative rings and give different interpretations of descent data. We consider in particular the case of Hopf–Galois extensions. When descent data exist, we classify them by non-Abelian cohomology sets and deduce a noncommutative version of Hilbert's Theorem 90.