Séminaire ART
organisé par l'équipe Algèbre, représentations, topologie
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Ningchuan Zhang
On the rationalization of the $\mathrm{K}(n)$-local determinant sphere
29 septembre 2026 - 14:00Salle de séminaires IRMA
Abstract: In chromatic homotopy theory, we study spectra one prime at a time by the height filtration of formal groups. One way to extract the height $n$ information is to localize at the Morava $\mathrm{K}$-theory $\mathrm{K}(n)$. In their recent breakthrough, Barthel—Schlank—Stapleton—Weinstein computed rational homotopy groups of the $\mathrm{K}(n)$-local sphere using $p$-adic arithmetic geometry. Building on their approach, we study the rational homotopy groups of the $\mathrm{K}(n)$-local determinant sphere and their relationship with Gross–Hopkins duality. This leads us to compute the rational group cohomology of $\mathrm{GL}_n(\mathbb{Z}_p)$ with coefficients in the Steinberg representation. The resulting Poincaré series agrees with the one predicted by the strong Chromatic Splitting Conjecture. This is joint work in progress with Tobias Barthel, Jacob Lerman, Guchuan Li, and Wei Yang. -
Frédéric Chapoton
TBA
6 octobre 2026 - 14:00Salle de séminaires IRMA
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Dani Kaufman
TBA
13 octobre 2026 - 14:00Salle de séminaires IRMA
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Chris Bowman
TBA
3 novembre 2026 - 14:00Salle de séminaires IRMA
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Sinan Yalin
TBA
10 novembre 2026 - 14:00Salle de séminaires IRMA
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Thomas Blom
TBA
17 novembre 2026 - 14:00Salle de séminaires IRMA
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Emmanuel Wagner
TBA
24 novembre 2026 - 14:00Salle de séminaires IRMA
TBA