Kato conjecture and motivic cohomology over finite fields - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: For an arithmetical scheme X, K. Kato introduced a certain complex ofGersten-Bloch-Ogus type whose component in degree a involves Galois cohomologygroups of the residue fields of all the points of X of dimension a. He stated aconjecture on its homology generalizing the fundamental exact sequences forBrauer groups of global fields. We prove the conjecture over a finite fieldassuming resolution of singularities. Thanks to a recently established resulton resolution of singularities for embedded surfaces, it implies theunconditional vanishing of the homology up to degree 4 for X projective smoothover a finite field. We give an application to finiteness questions for somemotivic cohomology groups over finite fields.



Author: Uwe Jannsen Univ. Regensburg, Shuji Saito Univ. of Tokyo

Source: https://arxiv.org/



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