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Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) | Einstein Institute of Mathematics

Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)

Date: 
Location: 
Ross 70
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications