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Fundamental, Picard, and Class Groups of Rings of Invariants

Published online by Cambridge University Press:  20 November 2018

Andy R. Magid
Andy R. Magid*
Affiliation:
The University of Oklahoma, Norman, Oklahoma
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Let G be a n affine algebraic group over the algebraically closed field k, and let V be an affine, normal algebraic variety over k on which G acts. Suppose that the ring of invariants k [F]G is finitely generated over k, and let W be the affine variety with k[W] = k[V]G. The purpose of this paper is to show that the induced homomorphism from the étale fundamental group of V to that of W is surjective, and to examine the consequences of this observation in terms of the relations between the Picard and divisor class groups of k[V] and k[W],

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 3 , 01 June 1976 , pp. 659 - 664
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Artin, M., Grothendieck topologies, Harvard Lecture Notes, 1962.Google Scholar
2. Lang, S., Algebra (Addison Wesley, Reading, Mass., 1965).Google Scholar
3. Fossum, R., The divisor class group of a krull domain (Springer-Verlag, New York, 1973).Google Scholar
4. Magid, A., Fundamental groups of products, Communications in Algebra 3 (1974), 37–46.Google Scholar
5. Murre, J. P., On the fundamental group, Tata Institute for Fundamental Research, Bombay, 1967.Google Scholar
6. Rosenlicht, M., On quotient varieties and the affine embedding of certain homogeneous spaces, Trans. Amer. Math. Soc. 101 (1967), 211–223.Google Scholar