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SUMMARY:Moduli of prismatic $(\\mathcal{G}\,\\mu)$-apertures [MPIM]
DTSTART:20250620T120500Z
DTEND:20250620T140000Z
DTSTAMP:20260415T093600Z
UID:indico-event-502@math-events.uni-bonn.de
DESCRIPTION:Speakers: Zachary Gardner (Boston College)\n\nOberseminar Arit
 hmetic Geometry and Representation Theory\nWe study the derived moduli sta
 ck $\\textup{BT}_n^{\\mathcal{G}\,\\mu}$ of (level-$n$ truncated) prismati
 c $(\\mathcal{G}\,\\mu)$-apertures\, where $\\mathcal{G}$ is a smooth affi
 ne group scheme over $\\mathbb{Z}_p$ and $\\mu$ is a $1$-bounded cocharact
 er of $\\mathcal{G}$ defined over an unramified extension of $\\mathbb{Z}_
 p$. Inspired by ideas of Drinfeld and Lau\, we show that $\\textup{BT}_n^{
 \\mathcal{G}\,\\mu}$ serves as a powerful group-theoretic generalization o
 f the moduli stack of ($n$-truncated) $p$-divisible groups\, endowed with 
 analogous smoothness\, finiteness\, and representability properties as wel
 l as natural analogues of Dieudonne theory and Grothendieck-Messing theory
 . This opens the door to an intrinsically group-theoretic study of Rapopor
 t-Zink spaces and potentially suggests new applications of derived algebra
 ic geometry to the study of $F$-zips. This is joint work with Keerthi Mada
 pusi.\n \n\nhttps://math-events.uni-bonn.de/event/502/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/502/
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