On non-realization results and conjectures of N. Kuhn

Nguyen The Cuong, et al. "On non-realization results and conjectures of N. Kuhn." Fundamenta Mathematicae 234.2 (2016): 139-161. <http://eudml.org/doc/286163>.

@article{NguyenTheCuong2016,
abstract = {We discuss two extensions of results conjectured by Nick Kuhn about the non-realization of unstable algebras as the mod-p singular cohomology of a space, for p a prime. The first extends and refines earlier work of the second and fourth authors, using Lannes’ mapping space theorem. The second (for the prime 2) is based on an analysis of the -1 and -2 columns of the Eilenberg-Moore spectral sequence, and of the associated extension. In both cases, the statements and proofs use the relationship between the categories of unstable modules and functors between $_\{p\}$-vector spaces. The second result in particular exhibits the power of the functorial approach.},
author = {Nguyen The Cuong, Gérald Gaudens, Geoffrey Powell, Lionel Schwartz},
journal = {Fundamenta Mathematicae},
keywords = {unstable modules; realization; Krull filtration; nilpotent filtration; nil-localization; Eilenberg-Moore spectral sequence},
language = {eng},
number = {2},
pages = {139-161},
title = {On non-realization results and conjectures of N. Kuhn},
url = {http://eudml.org/doc/286163},
volume = {234},
year = {2016},
}

TY - JOUR
AU - Nguyen The Cuong
AU - Gérald Gaudens
AU - Geoffrey Powell
AU - Lionel Schwartz
TI - On non-realization results and conjectures of N. Kuhn
JO - Fundamenta Mathematicae
PY - 2016
VL - 234
IS - 2
SP - 139
EP - 161
AB - We discuss two extensions of results conjectured by Nick Kuhn about the non-realization of unstable algebras as the mod-p singular cohomology of a space, for p a prime. The first extends and refines earlier work of the second and fourth authors, using Lannes’ mapping space theorem. The second (for the prime 2) is based on an analysis of the -1 and -2 columns of the Eilenberg-Moore spectral sequence, and of the associated extension. In both cases, the statements and proofs use the relationship between the categories of unstable modules and functors between $_{p}$-vector spaces. The second result in particular exhibits the power of the functorial approach.
LA - eng
KW - unstable modules; realization; Krull filtration; nilpotent filtration; nil-localization; Eilenberg-Moore spectral sequence
UR - http://eudml.org/doc/286163
ER -