Tensor generators on schemes and stacks

By Philipp Gross. 2013

50 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5b95c42e68f304c0e81c9409c374b3a4703ae4a3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Jack Hall
2. David Rydh
3. Jarod Alper
4. Philipp Gross
5. Daniel Halpern-Leistner
6. Chenyang Xu

In Statistical and Nonlinear Physics

1. David Rydh
2. Jack Hall
3. Jarod Alper

Citations in the corpus

• The étale local structure of algebraic stacks (2019, background): “Cor. 2.8]. 1.7.7. An algebraic stack Xis said to have the resolution property if every quasicoherent OX-module of finite type is a quotient of a locally free sheaf. By the main theorems of [Tot04] and [Gro17], a quasi-compact and quasi-separated algebraic stack is isomorphic to [U/GLN], where U is a ”