The purpose of this course is to give an introduction to étale cohomology.
Etale cohomology, a cohomology theory defined for schemes, is an algebraic analogue of singular cohomology and, in the case of fields, agrees with Galois cohomology. We plan to start with the definitions and properties of étale morphisms and Henselian rings, introduce necessary homological tools, learn the properties of étale cohomology, and if time permits, finish the course by outlining the proof of (some of) the Weil conjectures.
We assume some familiarity with schemes (for example, Section 1 to 4 of Chapter II of Hartshorne's Algebraic Geometry), but no prior knowledge on sheaves or homological algebra is needed. Course website at: