Title: Modules with q-connections (and sheared prismatization)


Abstract: Let X be a smooth p-adic formal scheme over Z_p. Given a ``framing'', that is  an etale map X ----> T to a torus,  Scholze defined the algebra D_q of q-differential operators on X. Though the algebra itself depends on the choice of a framing, Scholze conjectured in 2016 that the category of p-complete modules over it does not depend on X only and thus can be defined globally. Subsequently, in a joint  work with Bhatt, Scholze proved a weaker version of this conjecture for nilpotent  D_q-modules.  I will sketch a proof of the strong form of the conjecture.

The talk is based on a joint work with Bhatt, Kanaev, Mathew, Zhang, and myself.
 
Livestream link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=fd4d54d7-525f-4ce6-ab72-b2330104262b
Zoom link (for questions only; no video): https://huji.zoom.us/j/83127605942?pwd=vbVdV5UHwrtfcCH1Tvm10sBLzRo1s7.1