Motivic functors
Documenta mathematica, Tome 8 (2003), pp. 489-525
The notion of motivic functors refers to a motivic homotopy theoretic analog of continuous functors. In this paper we lay the foundations for a homotopical study of these functors. Of particular interest is a model structure suitable for studying motivic functors which preserve motivic weak equivalences and a model structure suitable for motivic stable homotopy theory. The latter model is Quillen equivalent to the category of motivic symmetric spectra. There is a symmetric monoidal smash product of motivic functors, and all model structures constructed are compatible with the smash product in the sense that we can do homotopical algebra on the various categories of modules and algebras. In particular, motivic cohomology is naturally described as a commutative ring in the category of motivic functors.
Classification :
14F42, 55P42
Mots-clés : motivic cohomology, motivic homotopy theory, functors of motivic spaces, homotopy functors
Mots-clés : motivic cohomology, motivic homotopy theory, functors of motivic spaces, homotopy functors
@article{10_4171_dm_148,
author = {Bj{\o}rn Ian Dundas and Oliver R\"ondigs and Paul Arne {\O}stv{\ae}r},
title = {Motivic functors},
journal = {Documenta mathematica},
pages = {489--525},
year = {2003},
volume = {8},
doi = {10.4171/dm/148},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/148/}
}
Bjørn Ian Dundas; Oliver Röndigs; Paul Arne Østvær. Motivic functors. Documenta mathematica, Tome 8 (2003), pp. 489-525. doi: 10.4171/dm/148
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