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Hasse-Schmidt derivations, divided powers and differential smoothness

 

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Author: Narváez Macarro, Luis
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2009
Published in: Annales de l'Institut Fourier, 59 (7), 2979-3014.
Document type: Article
Abstract: Let k be a commutative ring, A a commutative k-algebra and D the filtered ring of k-linear differential operators of A. We prove that: (1) The graded ring gr D admits a canonical embedding θ into the graded dual of the symmetric algebra of the module ΩA/k of differentials of A over k, which has a canonical divided power structure. (2) There is a canonical morphism ϑ from the divided power algebra of the module of k-linear Hasse-Schmidt integrable derivations of A to gr D. (3) Morphisms θ and ϑ fit into a canonical commutative diagram.
Cite: Narváez Macarro, L. (2009). Hasse-Schmidt derivations, divided powers and differential smoothness. Annales de l'Institut Fourier, 59 (7), 2979-3014.
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Format: PDF

URI: http://hdl.handle.net/11441/43077

DOI: 10.5802/aif.2513

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