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DTSTART:20070311T020000
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DTSTAMP:20261026T002911
DTSTART;TZID=America/Detroit:20261030T150000
DTEND;TZID=America/Detroit:20261030T160000
SUMMARY:Workshop / Seminar:Student Algebraic Geometry: Etale Homotopy and Higher Obstructions to Rational Points
DESCRIPTION:The étale topology on schemes is a testament to the influence of algebraic topology on algebraic geometry. Étale realizations of topological invariants\, such as the fundamental group and singular cohomology\, played a central role in the development of french-school algebraic geometry. This exposé will tell the story of the étale homotopy type of a scheme\, which provides a general framework for realizing homotopy-theoretic constructions in étale algebraic geometry. As an application of this\, I will present an obstruction theory for finding rational points on varieties. At the level of $\pi_1$ this theory will recover classical obstructions due to Grothendieck. I'll conclude with the question of exhibiting explicit examples in which the classical $\pi_1$-obstruction vanishes\, but higher obstruction classes prevent the existence of rational points.
UID:154077-21917127@events.umich.edu
URL:https://events.umich.edu/event/154077
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 2866
CONTACT:
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