Loops on schemes and the algebraic fundamental group

2021/09/23 by Kay Rülling, Stefan Schröer, Rülling, Kay +1 · 1 citation
Mathematics · #14E20 #14F35 #14H30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2109.11364

openalex publication_date 2021/09/23 · openalex created_date 2024/03/20 · openalex updated_date 2026/07/28

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.

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