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Abstract <p>We establish a derived functor characterization of the relative Spencer hypercohomology associated with a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{D}\)</EquationSource> <!--LobJMat2561111Rubtsov-m1--> </InlineEquation>-algebra corresponding to a formally integrable system of algebraic differential equations. Roughly speaking, this result can be interpreted as describing the global variation of solutions for the associated family of partial differential equations across fibers. Additionally, we provide an equivalent formulation in terms of a suitable Hochschild hypercohomology of the corresponding cosymbolic comodule.</p>

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Spencer Hypercohomologies in the Geometric Theory of Partial Differential Equations

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Jacob Kryczka,
  • Vladimir Rubtsov

摘要

Abstract

We establish a derived functor characterization of the relative Spencer hypercohomology associated with a \(\mathcal{D}\) -algebra corresponding to a formally integrable system of algebraic differential equations. Roughly speaking, this result can be interpreted as describing the global variation of solutions for the associated family of partial differential equations across fibers. Additionally, we provide an equivalent formulation in terms of a suitable Hochschild hypercohomology of the corresponding cosymbolic comodule.