Course Identification

Weil conjectures, exponential sums, etale morphisms and sheaves, etale site, fppf and fpqc topologies, descent, Zeta and L-functions, derived categories and functors, etale cohomology, etale fundamental group, Chow ring, cycle map, Chern classes, Brauer group, six functor formalism, base change theorems, Grothendieck--Lefschtez trace formula, function-sheaf dictionary, Grothendieck--Ogg--Shafarevich formula, comparison of etale and singular cohomology, local acyclicity, vanishing and nearby cycles, perverse sheaves.

The student will deepen their understanding of algebraic geometry and some of its cohomology theories. They will become acquainted with the Weil conjectures and other applications.

Stacks project: 10.143-4, 10.150-6, 15.44-5, 29.34-36, 34, 35, 37.8, 37.35-7, 41, 45, 49, 58, 59, 63, 64

Etale Cohomology Theory by Fu

Introduction to Etale Chomology by Tamme

Etale Cohomology and the Weil Conjecture by Freitag--Kiehl

Lectures on Etale Cohomology by Milne

Etale Cohomology by Milne

Weil Conjectrues, Perverse Sheaves and l-adic Fourier Transform by Kiehl--Weissauer