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Derived Moduli Spaces of Nonlinear PDEs II: Variational Tricomplex and BV Formalism

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arxiv 2406.16825 v1 pith:TI7IB7VJ submitted 2024-06-24 math.AG math.DG

Jacob Kryczka , Artan Sheshmani , Shing-Tung Yau This is my paper · ORCID
classification math.AGmath.DG
keywords deriveddifferentialnon-linearalgebro-geometricapplicationsboundarybv-formalismcalculus
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This paper is the second in a series of works dedicated to studying non-linear partial differential equations via derived geometric methods. We study a natural derived enhancement of the de Rham complex of a non-linear PDE via algebro-geometric techniques and examine its consequences for the functional differential calculus on the space of solutions. Applications to the BV-formalism with and without boundary conditions are discussed.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The $\mathcal{D}$-Geometric Hilbert Scheme -- Part I: Involutivity and Stability

    math.AG 2025-07 reject novelty 5.0 of 10

    A moduli-theoretic framework for PDEs via D-Hilbert schemes and Spencer stability is introduced, but the advertised refinement of Donaldson-Uhlenbeck-Yau is a restatement of the classical result.

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