Descent Theory for Vertex Algebras

C. R. Math. Rep. Acad. Sci. Canada Vol. 47 (4) 2025, pp. 36–56
(Received: 2025-10-29 , Revised: 2025-11-01)

Robin Mader, Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr., 80333 München, Germany; and Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1; email: rmader@ualberta.ca

Terry Gannon, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1; email: tjgannon@ualberta.ca

Arturo Pianzola, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1; email: a.pianzola@ualberta.ca

Abstract/Résumé:

Vertex algebras can be defined over any differential commutative ring. We develop the general descent theory for vertex algebras over such bases. We apply this to the classification of twisted forms of affine and Heisenberg vertex algebras, and to reinterpret and generalize a correspondence of Li.

Les algèbres vertex peuvent être définies sur tout anneau commutatif différentiel. On développe la théorie générale de la descente pour les algèbres vertex sur de telles bases. On applique celle-ci ensuite à la classification des formes tordues des algèbres vertex affines et de Heisenberg, et à la réinterprétation et à la généralisation d’une correspondance de Li.

Keywords: Descent, Group Schemes, Vertex Algebra

AMS Subject Classification: _ƒtale and other Grothendieck topologies and cohomologies, Group schemes, Vertex operators; vertex operator algebras and related structures 14F20, 14L15, 17B69

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