On prismatic cohomology and q-de Rham operators

Speaker: jingbang guo (Shanghai Center for Mathematical Sciences SCMS)

Time: 2025-11-03 15:00-18:00
Location: 1010, SIMIS

摘要：

 The prismatic cohomology, introduced first by Bhatt and Scholze, is a cohomology theory for p-adic formal schemes which can be specialized to many other cohomology theories.

In this talk, different approaches to prismatic cohomology will be briefly discussed, and more attention will be drawn to the prismatization, introduced by Drinfeld and Bhatt-Lurie, which realizes prismatic cohomology as coherent cohomology of certain stack. By taking suitable covering of this stack of prismatization, it is possible to study prismatic cohomology through concrete operators, for example, the so-called q-de Rham operators.

There will also be a general discussion, in terms of Hopf algebroids, on this process of extracting operators from stacks with suitable coverings, and in principle it should be nothing else but monadicity. There might also be a tentative discussion on the functoriality and duality for prismatic cohomology.

This talk is based on joint work with Ruochuan Liu and Guozhen Wang.