Integral cohomology of classical groups over a finite field
Copyright policy )Integral cohomology of classical groups over a finite field
Let \(G\) be one of the groups \(GL_n\), \(SL_n\), \(U_n\), \(SU_n\) or \(Sp\) over a finite field of characteristic \(p\). The author calculates the order of the integral Chern classes, obtained by Brauer lifting. The proof uses a description of the \(\text{mod }l\) cohomology of \(G\), for each prime \(l\) distinct from \(p\). For \(GL_n\) this description is done by \textit{D. Quillen} [Ann. Math., II. Ser. 96, 552-586 (1972; Zbl 0249.18022)]\ and for \(U_n\) and \(Sp\) by \textit{Z. Fiedorowicz} and \textit{S. Priddy} [Homology of classical groups over finite fields and their associated infinite loop spaces (Lect. Notes Math. 674, 1978; Zbl 0403.55010)]. The author computes this cohomology for the special groups \(SL_n\) and \(SU_n\).
- Cornell University United States
Algebra and Number Theory, Linear algebraic groups over finite fields, classical groups, integral Chern classes, cohomology, Brauer lifting, Cohomology theory for linear algebraic groups, finite field
Algebra and Number Theory, Linear algebraic groups over finite fields, classical groups, integral Chern classes, cohomology, Brauer lifting, Cohomology theory for linear algebraic groups, finite field
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