About: Perfect obstruction theory

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In algebraic geometry, given a Deligne–Mumford stack X, a perfect obstruction theory for X consists of: 1. * a perfect two-term complex in the derived category of quasi-coherent étale sheaves on X, and 2. * a morphism , where is the cotangent complex of X, that induces an isomorphism on and an epimorphism on . The notion was introduced by Kai Behrend and Barbara Fantechi for an application to the intersection theory on moduli stacks; in particular, to define a virtual fundamental class.

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  • In algebraic geometry, given a Deligne–Mumford stack X, a perfect obstruction theory for X consists of: 1. * a perfect two-term complex in the derived category of quasi-coherent étale sheaves on X, and 2. * a morphism , where is the cotangent complex of X, that induces an isomorphism on and an epimorphism on . The notion was introduced by Kai Behrend and Barbara Fantechi for an application to the intersection theory on moduli stacks; in particular, to define a virtual fundamental class. (en)
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  • 54594383 (xsd:integer)
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  • 3970 (xsd:nonNegativeInteger)
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  • 1039952241 (xsd:integer)
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dbp:author1Link
  • Kai Behrend (en)
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  • Barbara Fantechi (en)
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  • Barbara (en)
  • Kai (en)
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  • Behrend (en)
  • Fantechi (en)
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  • 1997 (xsd:integer)
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  • In algebraic geometry, given a Deligne–Mumford stack X, a perfect obstruction theory for X consists of: 1. * a perfect two-term complex in the derived category of quasi-coherent étale sheaves on X, and 2. * a morphism , where is the cotangent complex of X, that induces an isomorphism on and an epimorphism on . The notion was introduced by Kai Behrend and Barbara Fantechi for an application to the intersection theory on moduli stacks; in particular, to define a virtual fundamental class. (en)
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  • Perfect obstruction theory (en)
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