The connection between a conjecture of Carlisle and Kropholler, now a theorem of Benson and Crawley-Boevey, and Grothendieck's Riemann-Roch and duality theorems
The author shows that the essential points in the proof of the \textit{D. J. Benson} and \textit{W. W. Crawley-Boevey} theorem [Bull. Lond. Math. Soc. 27, No. 5, 435-440 (1995)], concerning the two top coefficients of the Poincaré series for the ring of invariants \(k[V]^G\) (where \(G\) is a finite group acting on a finite-dimensional vector space \(V\) linearly, \(k[V]\) is the symmetric algebra of \(V\)), can be derived from Grothendieck's Riemann-Roch theorem and the duality theorem.
Poincaré series for the ring of invariants
scientific article; zbMATH DE number 838574
scientific article