• Corpus ID: 244709278

Zeta-values of one-dimensional arithmetic schemes at strictly negative integers

  title={Zeta-values of one-dimensional arithmetic schemes at strictly negative integers},
  author={Alexey Beshenov},
Let X be an arithmetic scheme (i.e., separated, of finite type over SpecZ) of Krull dimension 1. For the associated zeta function ζ(X, s), we write down a formula for the special value at s = n < 0 in terms of the étale motivic cohomology of X and a regulator. We prove it in the case when for each generic point η ∈ X with charκ(η) = 0, the extension κ(η)/Q is abelian. We conjecture that the formula holds for any onedimensional arithmetic scheme. This is a consequence of the Weil-étale formalism… 

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