Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Special values of $L$-functions on regular arithmetic schemes of
  dimension $1$   We construct a well-behaved Weil-\'etale complex for a large class of
$\mathbb{Z}$-constructible sheaves on a regular irreducible scheme $U$ of
finite type over $\mathbb{Z}$ and of dimension $1$. We then give a formula for
the special value at $s=0$ of the $L$-function associated to any
$\mathbb{Z}$-constructible sheaf on $U$ in terms of Euler characteristics of
Weil-\'etale cohomology; for smooth proper curves, we obtain the formula of
arXiv:2009.14504. We deduce a special value formula for Artin $L$-functions
twisted by a singular irreducible scheme $X$ of finite type over $\mathbb{Z}$
and of dimension $1$. This generalizes and improves all results in
arXiv:1611.01720; as a special case, we obtain a special value formula for the
arithmetic zeta function of $X$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: econ