The Friedlander – Milnor Conjecture
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چکیده
Conjecture 32.1 is easily seen to be true for a torus (i.e., G G r m for some r 0), but even the simplest non-trivial case (that of G SL2 ) remains inaccessible. Guido and I published 5 papers together, all in some sense connected with this conjecture. We used the integral form GZ of a complex reductive algebraic group (which is a group scheme over Spec Z ) in order to form the group G(F) of points of G with values in a field F . Most of our joint work investigated various relations between G(C) and G(F) , the case F Fp (the algebraic closure of a prime field Fp ) being of special interest. One knows from considerations of étale cohomology that the cohomology of BG(C) with Z n coefficients is naturally isomorphic to that of the étale
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The Friedlander{Milnor Conjecture 1] asserts that if G is a reductive algebraic group over an algebraically closed eld k, then the comparison map H et (BG k ; Z=p) ?! H (BG; Z=p) is an isomorphism for all primes p not equal to the characteristic of k. Gabber's rigidity theorem 2] implies that this map is indeed an isomorphism for the stable general linear group GL (this is due to Suslin 6] for ...
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The Friedlander–Milnor Conjecture [1] asserts that if G is a reductive algebraic group over an algebraically closed field k, then the comparison map H ét(BGk,Z/p) −→ H (BG,Z/p) is an isomorphism for all primes p not equal to the characteristic of k. Gabber’s rigidity theorem [2] implies that this map is indeed an isomorphism for the stable general linear group GL (this is due to Suslin [6] for ...
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