Étale fundamental groups

Abstract: Motivated by topological considerations, one can define an algebraic analogue of the fundamental group, called the etale fundamental group. We will give a definition (via the abstract theory of Galois categories from SGA), and review some basic calculations.

References: Milne, Lectures on étale cohomology, Chapter 3; and/or Poonen, Rational points on varieties, Sections 3.5.9 and 3.5.11.

algebraic geometrynumber theory

Audience: advanced learners

( slides )

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STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.

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