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Annals of Mathematics, II. Series Vol. 150, No. 2, pp. 663728 (1999) 

General linear and functor cohomology over finite fieldsVincent Franjou, Eric M. Friedlander, Alexander Scorichenko and Andrei SuslinReview from Zentralblatt MATH: This paper contains many definite results concerning the cohomology of families of representations of $\text{GL}_n$ over a finite field $\bbfF_q$. A representation like the module $\wedge^2 \bbfF_q^n$ for $\text{GL}_n(\bbfF_q)$ makes sense for every $n$. Such a representation `for all $n$ simultaneously' is an object of the category $\Cal F$, or $\Cal F(\bbfF_q)$, of all functors from finitedimensional $\bbfF_q$ vector spaces to $\bbfF_q$ vector spaces, studied extensively by Franjou, Lannes and Schwarz. Similarly we have the category $\Cal P$, or $\Cal P(\bbfF_q)$, of `strict polynomial functors' introduced by {\it E. M. Friedlander} and {\it A. Suslin} [Invent. Math. 127, No. 2, 209270 (1997; Zbl 0918.20035)]. But the results of the authors are much stronger and much more explicit than in these works. Reviewed by Wilberd van der Kallen Keywords: polynomial functors; rational modules; algebraic groups; categories of functors; exponential functors; cohomology of representations; linear algebraic groups over finite fields; polynomial representations; cohomology rings; divided powers; symmetric powers; Ext groups Classification (MSC2000): 20G05 20G10 18G05 18A22 20J05 20G40 14L15 18G15 Full text of the article:
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