Universität Regensburg Mathematik Kato conjecture and motivic cohomology over finite fields

@inproceedings{Jannsen2009UniversittRM,
  title={Universit{\"a}t Regensburg Mathematik Kato conjecture and motivic cohomology over finite fields},
  author={Uwe Jannsen and Shuji Saito},
  year={2009}
}
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 conjecture 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 singularities. Thanks to a recently established result on resolution of singularities for… CONTINUE READING

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