Hasse–Schmidt modules versus integrable connections
We prove that, in characteristic 0, any Hasse–Schmidt module structure can be recovered from its underlying integrable connection, and consequently Hasse–Schmidt modules and modules endowed with an integrable connection coincide.
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| Published in: | Revista matemática complutense Vol. 34; no. 1; pp. 75 - 98 |
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| Language: | English |
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2021
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| Abstract | We prove that, in characteristic 0, any Hasse–Schmidt module structure can be recovered from its underlying integrable connection, and consequently Hasse–Schmidt modules and modules endowed with an integrable connection coincide. |
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| AbstractList | We prove that, in characteristic 0, any Hasse–Schmidt module structure can be recovered from its underlying integrable connection, and consequently Hasse–Schmidt modules and modules endowed with an integrable connection coincide. |
| Author | Narváez Macarro, Luis |
| Author_xml | – sequence: 1 givenname: Luis orcidid: 0000-0003-4316-5019 surname: Narváez Macarro fullname: Narváez Macarro, Luis email: narvaez@us.es organization: Departamento de Álgebra and Instituto de Matemáticas (IMUS), Facultad de Matemáticas, Universidad de Sevilla |
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| Cites_doi | 10.1017/S002776300002002X 10.1515/crll.1999.043 10.1080/00927870902828751 10.1090/S0002-9947-1963-0154906-3 10.5802/aif.2513 10.1515/9781400867318 10.1007/BFb0061194 10.1016/j.aim.2012.01.015 10.1007/BF02732123 |
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| Copyright | Universidad Complutense de Madrid 2019 Universidad Complutense de Madrid 2019. |
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| EndPage | 98 |
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| Keywords | 13N10 HS-structure Hasse–Schmidt derivation Substitution map Integrable connection 14F10 Differential operator 13N15 Integrable derivation |
| Language | English |
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| References | Narváez Macarro, L.: Rings of differential operators as enveloping algebras of Hasse–Schmidt derivations. J. Pure Appl. Algebra 224(1), 320–361 (2020) BrownWCOn the embedding of derivations of finite rank into derivations of infinite rankOsaka J. Math.1978153813895042980422.13007 HuebschmannJDuality for Lie-Rinehart algebras and the modular classJ. Reine Angew. Math.1999510103159169609310.1515/crll.1999.043 Berthelot, P., Ogus, A.: Notes on Crystalline Cohomology. Mathematical Notes, vol. 21. Princeton University Press, Princeton (1978) MatsumuraHIntegrable derivationsNagoya Math. J.19828722724567659310.1017/S002776300002002X MirzavaziriMCharacterization of higher derivations on algebrasComm. Algebra2010383981987265038310.1080/00927870902828751 Narváez Macarro, L.: Hasse–Schmidt derivations versus classical derivations. In: “A panorama of Singularities”. Contemporary Mathematics, Amer. Math. Soc., Providence, RI, to appear. (arXiv:1810.08075) Narváez MacarroLOn the modules of m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m$$\end{document}-integrable derivations in non zero characteristicAdv. Math.2012229527122740288914310.1016/j.aim.2012.01.015 Deligne, P.: Equations Différentielles à Points Singuliers Réguliers. Lecture Notes in Mathematics, vol. 163. Springer, Berlin (1970) Grothendieck, A.: Éléments de Géométrie Algébrique (Rédigés Avec la Collaboration de Jean Dieudonné): IV. Étude Locale des Schémas et de Morphismes de Schémas, Quatrième Partie. Publ. Math. Inst. Hautes Études Sci, vol. 32. Press University de France, Paris (1967) HasseHSchmidtFKNoch eine Begründung der theorie der höheren differrentialquotienten in einem algebraischen Funktionenkörper einer UnbestimmtenJ. Reine Angew. Math.19371772232390017.10101 Narváez MacarroLHasse-Schmidt derivations, divided powers and differential smoothnessAnn. Inst. Fourier (Grenoble)200959729793014264934410.5802/aif.2513 Matsumura, H.: Commutative Ring Theory. Cambridge Studies in Advanced Mathematics, vol. 8. Cambridge University Press, Cambridge (1986) Narváez Macarro, L.: On Hasse–Schmidt derivations: the action of substitution maps. In: “Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Festschrift for Antonio Campillo on the Occasion of his 65th Birthday”, 219–262. Springer International Publishing, Cham, 2018 RinehartGSDifferential forms on general commutative algebrasTrans. Am. Math. Soc.196310819522215490610.1090/S0002-9947-1963-0154906-3 340_CR14 340_CR12 L Narváez Macarro (340_CR11) 2012; 229 340_CR13 GS Rinehart (340_CR15) 1963; 108 L Narváez Macarro (340_CR10) 2009; 59 H Hasse (340_CR5) 1937; 177 H Matsumura (340_CR7) 1982; 87 340_CR8 J Huebschmann (340_CR6) 1999; 510 340_CR1 WC Brown (340_CR2) 1978; 15 M Mirzavaziri (340_CR9) 2010; 38 340_CR3 340_CR4 |
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| Snippet | We prove that, in characteristic 0, any Hasse–Schmidt module structure can be recovered from its underlying integrable connection, and consequently... |
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| SubjectTerms | Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Modules Topology |
| Title | Hasse–Schmidt modules versus integrable connections |
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