ZETA FUNCTIONS OF REGULAR ARITHMETIC SCHEMES AT s = 0

@article{Morin2014ZETAFO,
  title={ZETA FUNCTIONS OF REGULAR ARITHMETIC SCHEMES AT s = 0},
  author={Baptiste Morin},
  journal={Duke Mathematical Journal},
  year={2014},
  volume={163},
  pages={1263-1336}
}
  • B. Morin
  • Published 30 March 2011
  • Mathematics
  • Duke Mathematical Journal
Lichtenbaum conjectured in (22) the existence of a Weil-etale cohomology in order to describe the vanishing order and the special value of the Zeta function of an arithmetic scheme X at s = 0 in terms of Euler- Poincare characteristics. Assuming the (conjectured) finite generation of some motivic cohomology groups we construct such a cohomology theory for regular schemes proper over Spec(Z). In particular, we compute (uncon- ditionally) the right Weil-etale cohomology of number rings and… 

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