Symmetric Spaces over a Finite Field

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Let G be a (connected) reductive group defined over a finite field F q (q odd) with a given involution θ:GG defined over F q . The pair (G, θ) will be called a symmetric space (over F q), we shall fix a closed subgroup K of the fixed point set G θ such that K is defined over F q and K contains the identity component (G θ )0 of .

Dedicated to A. Grothendieck on his 60th birthday
Supported in part by the National Science Foundation.