Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
Let k be a field with a real embedding. We compare the motivic slice filtration of a motivic spectrum over Spec(k) with the C2 –equivariant slice filtration of its equivariant Betti realization, giving conditions under which realization induces an equivalence between the associated slice towers. In particular, we show that, up to reindexing, the towers agree for all spectra obtained from localized quotients of MGL and Mℝ, and for motivic Landweber exact spectra and their realizations. As a consequence, we deduce that equivariant spectra obtained from localized quotients of Mℝ are even in the sense of Hill and Meier, and give a computation of the slice spectral sequence converging to π∗,∗BP〈n〉∕2 for 1 ≤ n ≤∞.
Keywords: motivic homotopy, equivariant homotopy theory, slice filtration, slice spectral sequence
Heard, Drew 1
@article{10_2140_agt_2019_19_3641,
author = {Heard, Drew},
title = {On equivariant and motivic slices},
journal = {Algebraic and Geometric Topology},
pages = {3641--3681},
publisher = {mathdoc},
volume = {19},
number = {7},
year = {2019},
doi = {10.2140/agt.2019.19.3641},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.3641/}
}
Heard, Drew. On equivariant and motivic slices. Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3641-3681. doi: 10.2140/agt.2019.19.3641
Cité par Sources :