Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable maps and Hurwitz schemes in mixed characteristic   In this short note, we propose a definition of complete Hurwitz schemes (and
stacks) in mixed characteristic. We follow an idea of R. Pandharipande, and
define the complete Hurwitz stack as a substack of stable maps of degree d of
nodal pointed curves of genus g to the universal curve over the moduli stack of
stable pointed curves of genus h. This substack is simply the closure of the
locus of Hurwitz covers in characteristic 0.
  We describe in detail the reduction modulo 2 of the complete Hurwitz stack of
genus 1 double covers of the projective line. The result is wilder than you
would imagine in your wildest dreams.
  We end by speculating about a possible relationship with the work of
Abramovich-Vistoli about stable maps into Deligne-Mumford stacks.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: nlin