On the condensed homotopy type of a scheme

Speaker(s)

Marcin Lara

Affiliation

IM PAN

Language of the talk

English

Date

April 15, 2026, 10:30 a.m.

Room

room 4070

Title in Polish

Skondensowany typ homotopijny schematu

Seminar

Seminar Algebraic Topology

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Grothendieck's étale fundamental group is one of the central objects of study in arithmetic geometry. It has a "higher" refinement: the Artin-Mazur-Friedlander étale homotopy type, which allows one to speak about higher homotopy groups of an algebraic variety/scheme, even over finite fields. In recent years, the étale topology and its fundamental group were generalized by their "pro-étale" counterparts in the work of Bhatt–Scholze. In this talk, I will discuss a common refinement of the pro-étale fundamental group and the étale homotopy type that uses the "condensed mathematics" of Clausen–Scholze and Barwick–Haine. I will also briefly hint at a future direction that would possibly be also applicable to large classes of topological spaces. This is joint work with P. J. Haine, T. Holzschuh, C. Mair, L. Martini, and S. Wolf.
 

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