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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Finite generation of class groups of rings of invariants


Author: Andy R. Magid
Journal: Proc. Amer. Math. Soc. 60 (1976), 45-48
MSC: Primary 13D15; Secondary 20G30
MathSciNet review: 0427306
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Abstract: Let R be a normal affine domain over the algebraically closed field k, and let G be a connected algebraic group acting rationally on R. It is shown that the divisor class group of $ {R^G}$ is a homomorphic image of an extension of a subgroup of the class group of R by a subquotient of the character group of G. In particular, if R has finitely generated class group, so does $ {R^G}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0427306-0
Article copyright: © Copyright 1976 American Mathematical Society