Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A 'Darboux theorem' for derived schemes with shifted symplectic
  structure   We prove a 'Darboux theorem' for derived schemes with symplectic forms of
degree $k<0$, in the sense of Pantev, Toen, Vaquie and Vezzosi arXiv:1111.3209.
More precisely, we show that a derived scheme $X$ with symplectic form $\omega$
of degree $k$ is locally equivalent to (Spec $A,\omega'$) for Spec $A$ an
affine derived scheme whose cdga $A$ has Darboux-like coordinates in which the
symplectic form $\omega'$ is standard, and the differential in $A$ is given by
Poisson bracket with a Hamiltonian function $H$ in $A$ of degree $k+1$.
  When $k=-1$, this implies that a $-1$-shifted symplectic derived scheme
$(X,\omega)$ is Zariski locally equivalent to the derived critical locus
Crit$(H)$ of a regular function $H:U\to{\mathbb A}^1$ on a smooth scheme $U$.
We use this to show that the underlying classical scheme of $X$ has the
structure of an 'algebraic d-critical locus', in the sense of Joyce
arXiv:1304.4508.
  In the sequels arXiv:1211.3259, arXiv:1305.6428, arXiv:1312.0090,
arXiv:1504.00690, 1506.04024 we will discuss applications of these results to
categorified and motivic Donaldson-Thomas theory of Calabi-Yau 3-folds, and to
defining new Donaldson-Thomas type invariants of Calabi-Yau 4-folds, and to
defining 'Fukaya categories' of Lagrangians in algebraic symplectic manifolds
using perverse sheaves, and we will extend the results of this paper and
arXiv:1211.3259, arXiv:1305.6428 from (derived) schemes to (derived) Artin
stacks, and to give local descriptions of Lagrangians in $k$-shifted symplectic
derived schemes.
  Bouaziz and Grojnowski arXiv:1309.2197 independently prove a similar 'Darboux
Theorem'.

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The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph