Introduces filtered formal groups and Cartier duality, proves a G_m-equivariant degeneration via normal cone construction, establishes unicity of complete filtrations, recovers the MRT19 filtration, and studies lifts of G-hat-Hochschild homology to spectral algebraic geometry.
Derived Algebraic Geometry
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abstract
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
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Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.
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Filtered formal groups, Cartier duality, and derived algebraic geometry
Introduces filtered formal groups and Cartier duality, proves a G_m-equivariant degeneration via normal cone construction, establishes unicity of complete filtrations, recovers the MRT19 filtration, and studies lifts of G-hat-Hochschild homology to spectral algebraic geometry.
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The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds
Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.