Finite generation of class groups of rings of invariants
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- by Andy R. Magid PDF
- Proc. Amer. Math. Soc. 60 (1976), 45-48 Request permission
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 ${R^G}$.References
- Hyman Bass, Introduction to some methods of algebraic $K$-theory, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 20, American Mathematical Society, Providence, R.I., 1974. Expository Lectures from the CBMS Regional Conference held at Colorado State University, Ft. Collins, Colo., August 24-28, 1973. MR 0347942
- Maxwell Rosenlicht, Toroidal algebraic groups, Proc. Amer. Math. Soc. 12 (1961), 984–988. MR 133328, DOI 10.1090/S0002-9939-1961-0133328-9
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 45-48
- MSC: Primary 13D15; Secondary 20G30
- DOI: https://doi.org/10.1090/S0002-9939-1976-0427306-0
- MathSciNet review: 0427306