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arXiv · 1411.5831

Weight homology of motives

Shane Kelly·Shuji Saito
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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-Soul\'e'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 the first author's Ph.D. thesis arXiv:1305.5349 we do not have to restrict to smooth schemes.

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Shane Kelly, Shuji Saito. 2014-11-21. Weight homology of motives. https://arxiv.org/abs/1411.5831

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