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College of Liberal Arts and Sciences | Mathematics

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February 26, 2019 | 2:00 p.m. - 3:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Piotr Pstragowski, Northwestern University

Title: Chromatic homotopy is algebraic when p > n^2+n+1

Abstract:

In chromatic homotopy theory, one stratifies the stable homotopy category by fixing a prime and looking at the E(n)-local parts, which informally see "information up to height n". As the height grows, these categories become increasingly intricate and converge to the p-local homotopy theory in a precise sense. 

On the other hand, it has been observed that when the prime is large relative to the height, then the E(n)-local category simplifies considerably - for example, the E(n)-local homotopy groups of spheres admit a purely algebraic description.  

In this talk, we show that when p > n^2+n+1, the homotopy category of E(n)-local spectra is equivalent to the homotopy category of differential E(n)_* E(n)-comodules, giving a precise sense in which chromatic homotopy theory is algebraic at large primes. This extends the work of Bousfield at n = 1 to all heights, and affirms a conjecture of Franke.

For more information about this event, please contact Department of Mathematics at 3135772479 or math@wayne.edu.