Étale cohomology and étale homotopy

Aim

The goal of this conference is to bring together experts working on different aspects of étale cohomology and (stratified) étale homotopy. On the one hand, there has been a lot of activity in algebraic and arithmetic geometry on the study of cohomology, local systems, fundamental groups, and arithmetic representations. On the other hand, the development of higher category theory has allowed for the clarification, modernisation, and generalisation of the foundations of unstable étale homotopy theory. By bringing together experts from both sides, we want to share ideas and problems across the aisle and create new opportunities for collaboration.

Schedule and abstracts

The schedule is now available at this link.  Titles and abstracts are collected here.

A booklet containing all practical information (including the schedule, titles and abstract) has been prepared and you can dowload it at this link.

Lecture series

There will be two mini-courses, aimed at bridging the language gap and introducing some of the problems that people are thinking about.

Peter Haine (University of California, Berkeley)

Title: Étale homotopy theory and exodromy

Abstract: The goal of this mini-course is to give a modern introduction to étale homotopy theory. We’ll explain a number of different descriptions of the étale homotopy type and how they can be used to prove a number of foundational results. In particular, we’ll explain a description of the étale homotopy type coming from our work with Barwick and Glasman on exit-path categories in algebraic geometry. We’ll also explain some applications of étale homotopy theory.

Moritz Kerz (Universität Regensburg)

Title: The weight filtration and local systems

Abstract: Weight filtrations appear in various mathematical settings, including Hodge theory and the theory of local Galois representations. My talks will introduce an abstract framework clarifying why these filtrations form abelian categories with shared characteristics. We will then study families of pure structures on an algebraic curve over a local field (complex or non-archimedean). This gives rise to two settings leading to mixed objects: the degeneration of pure structures and the cohomology of pure structures over an affine curve.

Speakers

Tomoyuki Abe (Kavli IPMU)

Clark Barwick (University of Edinburgh)

Anna Cadoret (Université Sorbonne)

Hélène Esnault (Freie Universität Berlin)

Tim Holzschuh (Ruprecht-Karls-Universität Heidelberg)

Marcin Lara (IMPAN)

Massimo Pippi (Université d'Angers)

Emanuel Reinecke (IHES)

Jakob Scholbach (Università degli Studi di Padova)

Jean-Baptiste Teyssier (Université Sorbonne)

Sebastian Wolf (Universität Regensburg)

Organisers

Remy van Dobben de Bruyn (Universiteit Utrecht)

Katharina Hübner (Goethe-Universität Frankfurt)

Mauro Porta (Université Strasbourg)

Directions

All talks will take place in Lecture Hall 9 of the Auditorium Complex (Hörsaalgebäude) on the Bockenheim campus of Goethe-Universität Frankfurt. Click here for the building location on Google Maps. This is 10–15 minutes by public transit from the main train station.

From Frankfurt airport (FRA), there are frequent trains to the main station (Hauptbahnhof). The airport has separate train stations for regional travel (Regionalbahnhof) and long distance travel (Fernbahnhof). There are frequent trains to the city centre from both, taking about 10–15 minutes. The regional station is closer to the airport and regional trains are slightly cheaper.