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A note on the nonlinear derived Cauchy problem

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arxiv 2211.04860 v1 pith:KOEK7VLE submitted 2022-11-09 math.AG math.AP

Frédéric Paugam (SU , IMJ-PRG) This is my paper · ORCID
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keywords problemderivedanalyticcasecauchydefinenonlinearadapt
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We define and study a generalization of the analytic Cauchy problem, that specializes to the Cauchy-Kowaleskaya-Kashiwara problem in the linear case. The main leitmotive of this text is to adapt Kashiwara's formulation of this problem both to the relatively D-algebraic case and to the derived analytic situation. Along the way, we define the characteristic variety of a derived nonlinear partial differential system.

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  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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