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Trivialité des fibrés vectoriels équivariants pour les groupes abéliens finis

✍ Scribed by D. Castella

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
119 KB
Volume
151
Category
Article
ISSN
0001-8708

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✦ Synopsis

Let G be a finite abelian group, V a complex G-module, and A the algebra of all polynomial functions on V. We show that if M is a free A-module of finite rank, then there exists a G-module W such that M is isomorphic to A W. As a consequence all algebraic G-vector bundles with base V are trivial, and the action of G on the total space of such a bundle is linearizable.

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✍ Lionel Ducos 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 167 KB

It is well known that certain polynomials have an Abelian group as Galois group over rational function fields k(t) with characteristic not dividing the order of this group. Moreover, it is possible to realize all Abelian groups over k(t) in the fields k((t)). In this paper, we construct and calculat