Étale Fundamental Group
The étale fundamental group encodes finite étale covers through automorphisms of a geometric fibre functor. Read the classification theorem alongside the spectrum-of-a-field example to connect geometric covering theory with Galois theory.
Before opening the references
Where to read
Start here: The Stacks Project — Fundamental groups
The Stacks Project Authors · Online reference · English · Free full text
Section 58.6, Definition 58.6.1, Theorem 58.6.2, and Lemma 58.6.3
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Algebraic Geometry in the library · Preparation and skip guidance