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• W1585460488 abstract "37 Abstract. For an arithmetical scheme X, K. Kato introduced a certain complex of Gersten-Bloch-Ogus type whose component in degree a involves Galois cohomology groups of the residue fields of all the points of X of dimension a. He stated a con- jecture on its homology generalizing the fundamental exact sequences for Brauer groups of global fields. We prove the conjecture over a finite field assuming resolution of singular- ities. Thanks to a recently established result on resolution of singularities for embedded surfaces, it implies the unconditional vanishing of the homology up to degree 4 for X projective smooth over a finite field. We give an application to finiteness questions for some motivic cohomology groups over finite fields." @default.
• W1585460488 created "2016-06-24" @default.
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• W1585460488 date "2009-10-15" @default.
• W1585460488 modified "2023-10-01" @default.
• W1585460488 title "Kato conjecture and motivic cohomology over finite fields" @default.
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