Loops on schemes and the algebraic fundamental group
Algebraic Geometry
2024-03-19 v2
Abstract
In this note we give a re-interpretation of the algebraic fundamental group for proper schemes that is rather close to the original definition of the fundamental group for topological spaces. The idea is to replace the standard interval from topology by what we call interval schemes. This leads to an algebraic version of continuous loops, and the homotopy relation is defined in terms of the monodromy action. Our main results hinge on Macaulayfication for proper schemes and Lefschetz type results.
Cite
@article{arxiv.2109.11364,
title = {Loops on schemes and the algebraic fundamental group},
author = {Kay Rülling and Stefan Schröer},
journal= {arXiv preprint arXiv:2109.11364},
year = {2024}
}
Comments
title changed, to appear in Rev. Mat. Complut