Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weil-etale Cohomology and Special Values of L-functions   We construct the Weil-\'etale cohomology and Euler characteristics for a
subclass of the class of $\mathbb{Z}$-constructible sheaves on an open
subscheme of the spectrum of the ring of integers of a number field. Then we
show that the special value of an Artin L-function of toric type at zero is
given by the Weil-\'etale Euler characteristic of an appropriate
$\mathbb{Z}$-constructible sheaf up to signs. As applications of our result, we
will prove a formula for the special value of the L-function of an algebraic
torus at zero which is similar to Ono's Tamagawa Number Formula.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th