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

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

## Date:

Sunday, 19 January, 2020 - 16:00 to 18:00

Repeats every week every Sunday until Sat Feb 01 2020 except Sun Oct 27 2019

## Location:

Ross 70