Model categorical Koszul-Tate resolution for algebras over differential operators

Gennaro di Brino; Damjan Pistalo; Norbert Poncin

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arXiv · 1505.07964

Model categorical Koszul-Tate resolution for algebras over differential operators

Gennaro di Brino·Damjan Pistalo·Norbert Poncin

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Abstract

Derived D-Geometry is considered as a convenient language for a coordinate-free investigation of nonlinear partial differential equations up to symmetries. One of the first issues one meets in the functor of points approach to derived D-Geometry, is the question of a model structure on the category C of differential non-negatively graded quasi-coherent commutative algebras over the sheaf D of differential operators of an appropriate underlying variety. In [BPP15a], we described a cofibrantly generated model structure on C via the definition of its weak equivalences and its fibrations. In the present article - the second of a series of works on the BV-formalism - we characterize the class of cofibrations, give explicit functorial cofibration-fibration factorizations, as well as explicit functorial fibrant and cofibrant replacement functors. We then use the latter to build a model categorical Koszul-Tate resolution for D-algebraic on-shell function algebras.

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Gennaro di Brino, Damjan Pistalo, Norbert Poncin. 2015-05-29. Model categorical Koszul-Tate resolution for algebras over differential operators. https://arxiv.org/abs/1505.07964

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