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 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 .

**[1]**Hyman Bass,*Introduction to some methods of algebraic 𝐾-theory*, 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; Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 20. MR**0347942****[2]**Maxwell Rosenlicht,*Toroidal algebraic groups*, Proc. Amer. Math. Soc.**12**(1961), 984–988. MR**0133328**, 10.1090/S0002-9939-1961-0133328-9

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1976-0427306-0

Article copyright:
© Copyright 1976
American Mathematical Society