Holmstrom Realizations

See the last section of Levine’s K-theory handbook chapter. He discusses “realization functors” for various kinds of categories of motives, and various cohomology theories. Seems really interesting.

Realizations can also refer to maps relating A1-homotopy theory to classical homotopy theory. See end of chapter 3 in Morel-Voevodsky: A1-homotopy theory of schemes.


K-th 992 : Réalisations des complexes motiviques de Voevodsky by Florence Lecomte and Nathalie Wach

In this paper, we construct realizations of motivic complexes over a number field. The De Rham realization is represented by a motivic De Rham complex and has a Hodge filtration. The Betti and l-adic realizations are integrally defined. When restricted to geometrical motives, the realization functors are endowed with Bondarko’s weight filtration and rationally agree with Huber’s realizations.

nLab page on Realizations

Created on June 9, 2014 at 21:16:13 by Andreas Holmström