Oberseminar Lecture-Shane Kelly

Motivic homology theories

Abstract: This is joint work with Shuji Saito. Using work of Bondarko, we identify additive functors on Chow motives with a class of homological functors on Voevodsky's motives. Using this identification, we define a "weight" homology functor, which in special cases, recovers Gillet-Soulés weight homology, and Geisser's Kato-Suslin homology. We also mention the "field of constants" part of a motive as defined by Ayoub and Barbieri-Viale, and the canonical homology theory which calculates the difference between the motivic homology and étale motivic homology of a motive, and explain how these are all connected over a finite field.