Deformation theory of representable morphisms of algebraic stacks

DOI10.1007/s00209-005-0875-9zbMath1096.14007OpenAlexW1994704226MaRDI QIDQ2491112

Martin C. Olsson

Publication date: 26 May 2006

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-005-0875-9

Mathematics Subject Classification ID

Formal methods and deformations in algebraic geometry (14D15) Generalizations (algebraic spaces, stacks) (14A20)

Related Items (30)

Strong rational connectedness of surfaces ⋮ The moduli of sections has a canonical obstruction theory ⋮ Complete moduli spaces of branchvarieties ⋮ Presenting higher stacks as simplicial schemes ⋮ Artin's criteria for algebraicity revisited ⋮ Deformation of formal schemes through local homology ⋮ A wall-crossing formula for Gromov-Witten invariants under variation of git quotient ⋮ Artin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts ⋮ Logarithmic quasimaps ⋮ Autoequivalences of twisted K3 surfaces ⋮ The Hilbert stack ⋮ Tame stacks in positive characteristic ⋮ Arakelov-Parshin rigidity of towers of curve fibrations ⋮ Twisted stable maps to tame Artin stacks ⋮ Quantum Kirwan morphism and Gromov-Witten invariants of quotients. II ⋮ Openness of versality via coherent functors ⋮ Deformation of a smooth Deligne-Mumford stack via differential graded Lie algebra ⋮ On the local quotient structure of Artin stacks ⋮ Logarithmic Gromov-Witten invariants ⋮ \(\underline{\Hom}\)-stacks and restriction of scalars ⋮ The resolution property via Azumaya algebras ⋮ Virtual cycles of stable (quasi-)maps with fields ⋮ Stable pairs with a twist and gluing morphisms for moduli of surfaces ⋮ The Picard functor of an algebraic stack ⋮ Coherent Tannaka duality and algebraicity of Hom-stacks ⋮ Stable points on algebraic stacks ⋮ The logarithmic cotangent complex ⋮ Existence of slices on a tame context ⋮ Hom stacks ⋮ Stringy invariants and toric Artin stacks

Cites Work

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• Algebraic spaces
• Complexe cotangent et déformations. I. (The cotangent complex and deformations. I.)
• Séminaire de géométrie algébrique du Bois Marie 1960/61 (SGA 1), dirigé par Alexander Grothendieck. Augmenté de deux exposés de M. Raynaud. Revêtements étales et groupe fondamental. Exposés I à XIII. (Seminar on algebraic geometry at Bois Marie 1960/61 (SGA 1), directed by Alexander Grothendieck. Enlarged by two reports of M. Raynaud. Ètale coverings and fundamental group)
• Théorie de Hodge. III
• Complexe cotangent et déformations. II
• The logarithmic cotangent complex
• Sheaves on Artin stacks
• Deformation theory of algebraic stacks

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