Aspects of motivic cohomology - Matthew Morrow

2021 Graduate Summer School

Topic: Aspects of motivic cohomology
Speaker: Matthew Morrow
Affiliation: IMJ-PRG
Date: July 15, 2021

Motivic cohomology offers, at least in certain situations, a geometric refinement of algebraic K-theory or its variants (G-theory, KH-theory, étale K-theory,…). We will overview some aspects of the subject, ranging from the original cycle complexes of Bloch, through Voevodsky’s work over fields, to more recent p-adic developments in the arithmetic context where perfectoid and prismatic techniques appear.

Prerequisites: Algebraic geometry, sheaf theory, cohomology. Comfort with derived techniques such as descent and the cotangent complex would be helpful. Casual familiarity with K-theory, cyclic homology, and their variants would be motivational. Infinity-categories and spectra will appear, though probably not in a very essential way.