Considering a (co)homology theory T on a base category C as a fragment of a first-order logical theory we here construct an abelian category A[T] which is universal with respect to models of T in abelian categories. Under mild conditions on the base category C, e.g. for the category of algebraic schemes, we get a functor from C to Ch(Ind(A[T])) the category of chain complexes of ind-objects of A[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(Ind(A[T])) to Voevodsky's motivic complexes.

T-motives / L. Barbieri-Viale. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 221:7(2017 Jul 01), pp. 1565-1588. [10.1016/j.jpaa.2016.12.017]

T-motives

L. Barbieri-Viale
2017

Abstract

Considering a (co)homology theory T on a base category C as a fragment of a first-order logical theory we here construct an abelian category A[T] which is universal with respect to models of T in abelian categories. Under mild conditions on the base category C, e.g. for the category of algebraic schemes, we get a functor from C to Ch(Ind(A[T])) the category of chain complexes of ind-objects of A[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(Ind(A[T])) to Voevodsky's motivic complexes.
algebra; motives; topos
Settore MAT/02 - Algebra
1-lug-2017
26-gen-2017
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/472748
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