Tensor generators on schemes and stacks
| Autor: | Philipp Gross |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Structure (category theory) Vector bundle General linear group Frame bundle Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Scheme (mathematics) FOS: Mathematics Geometry and Topology Tensor Affine transformation Algebraic Geometry (math.AG) Quotient Mathematics |
| Zdroj: | Algebraic Geometry. :501-522 |
| ISSN: | 2214-2584 |
| Popis: | We show that an algebraic stack with affine stabilizer groups satisfies the resolution property if and only if it is a quotient of a quasi-affine scheme by the action of the general linear group, or equivalently, if there exists a vector bundle whose associated frame bundle has quasi-affine total space. This generalizes a result of B. Totaro to non-normal and non-noetherian schemes and algebraic stacks. Also, we show that the vector bundle induces such a quotient structure if and only if it is a tensor generator in the category of quasi-coherent sheaves. 22 pages, complete overhaul of paper |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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