## Student Arithmetic Geometry Seminar: The Saturated De Rham-Witt complex, after Bhatt, Lurie, Mathew

Seminar | December 6 | 4:10-5 p.m. | 891 Evans Hall

Arthur Ogus, UC Berkeley

Department of Mathematics

Let $X/k$ be a smooth scheme over a perfect field of characteristic $p$. The de Rham-Witt complex, constructed by Illusie (with roots in work by Bloch, Lubkin, and Deligne) is a canonical sheaf of differential graded algebras on the Zariski site which computes the crystalline cohomology of $X/W$ and which reveals a great deal of information about the action of the Frobenius endomorphism of $X$. Bhatt, Lurie, and Mathew have recently given a simple new construction of this complex which, unlike the original, seems to give reasonable answers for some singular schemes. I will explain the main points of the new construction and how it works for schemes with toric singularities.

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