Abstract
In the first half of this article we define a new weight homology functor on Voevodsky’s category of effective motives, and investigate some of its properties. In special cases we recover Gillet-Soule’s weight homology, and Geisser’s Kato-Suslin homology. In the second half, we consider the notions of “co-etale” and “reduced” motives, and use the notions to a prove a theorem comparing motivic homology to etale motivic homology. Due to [Ke1] we do not have to restrict to smooth schemes.
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