Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology of moduli spaces of curves of genus three via point counts   In this article we consider the moduli space of smooth $n$-pointed
non-hyperelliptic curves of genus 3. In the pursuit of cohomological
information about this space, we make $\mathbb{S}_n$-equivariant counts of its
numbers of points defined over finite fields for $n \leq 7$. Combining this
with results on the moduli spaces of smooth pointed curves of genus 0, 1 and 2,
and the moduli space of smooth hyperelliptic curves of genus 3, we can
determine the $\mathbb{S}_n$-equivariant Galois and Hodge structure of the
($\ell$-adic respectively Betti) cohomology of the moduli space of stable
curves of genus 3 for $n \leq 5$ (to obtain $n \leq 7$ we would need counts of
``8-pointed curves of genus 2'').

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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph