Étale Fundamental Groups: a geometric and topological approach to fundamental groups in algebraic geometry
Year: 2026
Type: preprint
Abstract: This thesis explores the notion of fundamental groups across three mathematical settings. We begin with the classical topological theory of covering spaces, highlighting its structural analogy with Galois theory. We then follow Grothendieck in transporting these ideas to algebraic geometry. The inadequacy of the Zariski topology motivates the étale topology, from which the étale fundamental group is constructed and compared to its topological counterpart via transcendental methods. Finally, we linearise the theory through Tannakian duality, where fundamental groups are recovered as automorphism groups of fibre functors on certain monoidal categories, a framework broad enough to encompass étale, topological, and motivic Galois groups alike.
Source: arXiv (Cornell University)
Author: De Vos, Loris
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165755766