Year: 2020
Type: preprint
Abstract: We extend the notion of rational points and cohomological obstructions on varieties to categories fibred in groupoids. We also establish the generalized theory of descent by torsors. Then we interpret the obstruction given by the second cohomology of abelian sheaves in terms of categorical points of gerbes, analogue to descent by torsors. As an application, we construct some composite obstructions not larger than the descent obstruction. We also propose some new kinds of obstructions including the derived obstruction, which has good behavior under a product and is also not larger than the descent obstruction.
Source: arXiv (Cornell University)
Author: Lv, Chang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5861458596
OpenAlex ID: W3085301061