On the motivic cohomology of schemes

Abstract: I will report on joint work with Matthew Morrow. Using ideas from topological cyclic homology and $p$-adic Hodge theory, we construct a theory of $p$-adic motivic complexes for any qcqs scheme in characteristic $p$. This can be viewed as a generalization of algebraic cycles to singular, possibly nonreduced, schemes. A key result is an agreement of this construction with Bloch cycle complexes on smooth varieties which, time permitting, I will explain a proof of.

number theory

Audience: researchers in the topic

Columbia CUNY NYU number theory seminar