Quadratic forms and Clifford algebras on derived stacks
| Autor: | Gabriele Vezzosi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Clifford algebras
Derived algebraic geometry Quadratic forms Mathematics (all) Pure mathematics Group (mathematics) General Mathematics 010102 general mathematics Clifford algebra 01 natural sciences Mathematics - Algebraic Geometry Quadratic equation 0103 physical sciences FOS: Mathematics Derived stack Algebraic Topology (math.AT) 010307 mathematical physics Affine transformation Mathematics - Algebraic Topology 0101 mathematics Algebraic Geometry (math.AG) Mathematics |
| Popis: | In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We define the associated notion of derived Clifford algebra, in all these contexts, and compare it with its classical version, when they both apply. Finally, we prove three main existence results for derived shifted quadratic forms over derived stacks, define a derived version of the Grothendieck-Witt group of a derived stack, and compare it to the classical one. 42 pages; revised version to appear in Advances in Math |
| Databáze: | OpenAIRE |
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