Geodesic
Cup Products in Sheaf Cohomology
Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 469-477

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DOI

Let k be an algebraically closed field, and let l be a prime number not equal to char(k). Let X be a locally fibrant simplicial sheaf on the big étale site for k, and let Y be a k scheme which is cohomologically proper. Then there is a Künneth-type isomorphism which is induced by an external cup-product pairing. Reductive algebraic groups G over k are cohomologically proper, by a result of Friedlander and Parshall. The resulting Hopf algebra structure on may be used together with the Lang isomorphism to give a new proof of the theorem of Friedlander-Mislin which avoids characteristic 0 theory. A vanishing criterion is established for the Friedlander-Quillen conjecture.
DOI : 10.4153/CMB-1986-074-2
Mots-clés : 14F20, 18F25 
Jardine, J. F. Cup Products in Sheaf Cohomology. Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 469-477. doi: 10.4153/CMB-1986-074-2
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     title = {Cup {Products} in {Sheaf} {Cohomology}},
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     year = {1986},
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     number = {4},
     doi = {10.4153/CMB-1986-074-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-074-2/}
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