# A Darboux theorem for derived schemes with shifted symplectic structure

@article{Brav2018ADT,
title={A Darboux theorem for derived schemes with shifted symplectic structure},
author={Christopher Brav and Vittoria Bussi and Dominic Joyce},
journal={Journal of the American Mathematical Society},
year={2018}
}
• Published 27 May 2013
• Computer Science
• Journal of the American Mathematical Society
<p>We prove a Darboux theorem for derived schemes with symplectic forms of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k greater-than 0"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">k>0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, in the sense of Pantev, Toën, Vaquié, and…
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Let there be a smooth scheme over an algebraically closed field of characteristic zero, and be a regular function, and write inline-formula content-type "math/mathml".
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Let $f:U\to{\mathbb A}^1$ be a regular function on a smooth scheme $U$ over a field $\mathbb K$. Pantev, Toen, Vaquie and Vezzosi (arXiv:1111.3209, arXiv:1109.5213) define the "derived critical
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