A d-shifted Darboux theorem

2013/09/09 by Emile Bouaziz, Bouaziz, E., I. Grojnowski +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1309.2197

openalex publication_date 2013/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We give a local model for d-shifted symplectic dg-schemes, or Deligne-Mumford dg-stacks [PTVV]. Locally any such is a product of a "twisted shifted cotangent bundle", where the twist is given by an element df, with f ∈ H^1-d(\Cal O), and a quadratic bundle in middle degree. The latter only occurs if d = 4r+2.

Citations

• Shifted Symplectic Structures

Cited by

• (-1)-Shifted Darboux theorem of derived schemes in characteristic p>2
• Counting sheaves on Calabi-Yau 4-folds, I
• An outline of shifted Poisson structures and deformation quantisation in derived differential geometry

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