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Comparing the motives of Voevodsky and Nori

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Daniel Harrer (Freiburg)

What
  • SFB-Kolloquium
When Jan 28, 2016
from 03:30 pm to 04:30 pm
Where Mainz, 05-432 (Hilbertraum)
Contact Name Blickle
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Abstract.

The aim of this talk is to compare two rather different categories of motives, those of Vladimir Voevodsky and Madhav Nori. We begin by explaining the general ideas behind them and then construct a comparison functor.

The proof has three main ingredients which we will explain:

1. translating finite correspondences, i.e. cycles, to so-called multi-valued morphisms,

2. a theory of étale covers on diagrams of finite correspondences,

3. a homological analogue of topological cell-structures on both varieties and finite correspondences.

 This approach should be seen as a generalisation of an earlier one by Annette Huber and Stefan Müller-Stach, but it is significantly complicated by the presence of finite correspondences.