Frobenius generation for algebraic stacks
Pat Lank, Fei Peng

TL;DR
This paper studies how the Frobenius morphism can generate generators for derived categories of algebraic stacks in positive characteristic, providing bounds and conditions for classical or strong generation.
Contribution
It introduces new methods to produce generators via Frobenius pushforwards and establishes bounds for Deligne--Mumford stacks.
Findings
Frobenius pushforwards can generate derived categories in many cases.
Bounds are provided for the number of Frobenius iterations needed.
The work applies to algebraic stacks in positive characteristic.
Abstract
This work investigates the Frobenius morphism on derived categories associated with algebraic stacks in positive characteristic. Particularly, we show that in many cases sufficiently many Frobenius pushforwards of a compact generator produce a classical or strong generator for the bounded derived category of coherent sheaves. In the case of Deligne--Mumford stacks, we can bound the number of iterates required.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory
