
TL;DR
This paper proposes a framework using topos theory to analyze Weil-type cohomology theories and motives, aiming to construct classifying toposes and a unifying syntactic triangulated category.
Contribution
It introduces a novel topos-theoretic framework for motives and cohomology theories, including the construction of a syntactic triangulated category linking to classical cohomologies.
Findings
Framework based on atomic two-valued toposes and homogeneous models
Preliminary results towards classifying toposes of Weil-type cohomologies
Construction of a syntactic triangulated category
Abstract
We present a research programme aimed at constructing classifying toposes of Weil-type cohomology theories and associated categories of motives, and introduce a number of notions and preliminary results already obtained in this direction. In order to analyze the properties of Weil-type cohomology theories and their relations, we propose a framework based on atomic two-valued toposes and homogeneous models. Lastly, we construct a syntactic triangulated category whose dual maps to the derived categories of all the usual cohomology theories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
