## Basics of étale and $\ell$-adic cohomology

Time: Thursdays, 2:15-3:45pm

Venue: room 1780 at MIMUW

Organizers: Piotr Achinger (IMPAN), Alexander Youcis (IMPAN), Marcin Lara (IMPAN)

#### Description

The seminar is aimed at undergraduate and graduate students and postdocs interested in algebraic and arithmetic geometry.

The topic for the Fall semester is Basics of étale and $\ell$-adic cohomology. The seminar syllabus is here: [PDF].

For future reference, the list of other topics we considered is here: [PDF].

The first talk will be given on Oct 10 by a subset of the organizers. We will give an outline of what we plan to do this semester and assign speakers to the talks.

 Oct 3 – Organizational meeting Oct 10 Piotr Achinger Introduction and overview Oct 17 Przemysław Grabowski Morphisms (étale, flat, unramified, smooth) Oct 24 Paweł Poczobut The étale fundamental group (I) Oct 31 No seminar Nov 7 Mykola Shamaiev The étale fundamental group (II) Nov 14 Paweł Poczobut The étale topology (I) Nov 21 Maciej Gałązka The étale topology (II) Nov 28 Przemysław Grabowski Cohomology of curves and abelian varieties Dec 5 Alex Youcis Artin comparison and Artin vanishing Dec 12 No seminar – Algebraic Groups Days Dec 19 Paweł Poczobut Proper base change and nearby cycles Christmas break Jan 9 Marcin Lara Properties of $\ell$-adic cohomology Jan 16 Piotr Rudnicki Cohomology over finite fields. Lefschetz trace formula and the Weil conjectures Jan 23 Jędrzej Garnek Purity and the Riemann hypothesis