Geodesic
Fundamental, Picard, and Class Groups of Rings of Invariants
Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 659-664

Voir la notice de l'article provenant de la source Cambridge University Press

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], 
Magid, Andy R. Fundamental, Picard, and Class Groups of Rings of Invariants. Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 659-664. doi: 10.4153/CJM-1976-066-4
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