Number theory learning seminar 2016-2017

The seminar will meet Wednesdays 1:30--3:30pm in Room 384H. This year's seminar will focus on etale cohomology, the goal being to understand Laumon's proof of the main theorem of Deligne's Weil II paper that gave a powerful and vast generalization of the Riemann Hypothesis over finite fields. Familiarity with various basic topics in arithmetic geometry (schemes, class field theory, derived categories, etc.) whenever needed to get through a lecture in finite time.

In the fall we will largely focus on understanding key examples and calculations as well as proofs of serious theorems concerning etale sheaf theory, aiming to get through much of Chapter 1 of the book of Freitag and Kiehl. That will get us through the important smooth and proper base change theorems, as well as the basic formalism of l-adic cohomology. In the winter we will delve further into the cohomology theory (especially to duality theorems and Kunneth formulas), and then move on to Laumon's technique of l-adic Fourier transforms in the sheaf setting.

Here are some references relevant to this year's seminar (in approximate order of appearance):

Some notes that Conrad wrote long ago that we will be following as the template for the fall and winter (supplemented by other references for omitted details indicated therein); this is an edited .pdf file, explaining some occasional (irrelevant) blank spaces in the middle of text
[FK] "Etale Cohomology and the Weil Conjectures" by Freitag and Kiehl
[Mi] "Etale Cohomology" by Milne
[KW] "Weil Conjectures, Perverse Sheaves, and l-adic Fourer transform" by Kiehl and Weissauer
[M1] "Analytic etale duality" (preprint) and [M2] "q-crystalline cohomologies" (in preparation) by Masullo

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Notes -- use at your own risk.

These are informal notes. They may change without warning.

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