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Vadim Vologodsy, University of Chicago and HSE


Title: Sheared prismatization


Abstract: In their work on prismatic cohomology,  Bhatt and Scholze   constructed  deformations of the category of modules with nilpotent integrable connection on p-adic varieties. Here the word ``nilpotent'' means that the p-curvature of the mod p reduction of the connection is locally nilpotent. I will explain how to extend the Bhatt-Scholze construction to all modules.  As an application, I will indicate a proof of a conjecture by Peter Scholze on q-connections. If time permits, I will also describe some applications to p-adic Simpson correspondence.  
 

The talk is based on a joint work in progress with Bhargav Bhatt, Artem Kanaev, Akhil Mathew, and Mingjia Zhang.

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