T-motives
| Autor: | Luca Barbieri-Viale |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Algebra and Number Theory
Functor 010102 general mathematics Mathematics - Category Theory Mathematics - Logic Homology (mathematics) 01 natural sciences Mathematics::Algebraic Topology Combinatorics Base (group theory) Mathematics - Algebraic Geometry Chain (algebraic topology) Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences Mathematics - K-Theory and Homology 010307 mathematical physics Abelian category 0101 mathematics Algebraic number Abelian group Complex number Mathematics |
| Popis: | Considering a (co)homology theory $\mathbb{T}$ on a base category $\mathcal{C}$ as a fragment of a first-order logical theory we here construct an abelian category $\mathcal{A}[\mathbb{T}]$ which is universal with respect to models of $\mathbb{T}$ in abelian categories. Under mild conditions on the base category $\mathcal{C}$, e.g. for the category of algebraic schemes, we get a functor from $\mathcal{C}$ to ${\rm Ch}({\rm Ind}(\mathcal{A}[\mathbb{T}]))$ the category of chain complexes of ind-objects of $\mathcal{A}[\mathbb{T}]$. This functor lifts Nori's motivic functor for algebraic schemes defined over a subfield of the complex numbers. Furthermore, we construct a triangulated functor from $D({\rm Ind}(\mathcal{A}[\mathbb{T}]))$ to Voevodsky's motivic complexes. Comment: Added reference to arXiv:1604.00153 [math.AG] |
| Databáze: | OpenAIRE |
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