TY - JOUR
T1 - The Bousfield-Kuhn functor and topological André-Quillen cohomology
AU - Behrens, Mark
AU - Rezk, Charles
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological André-Quillen cohomology of the K(n)-local Spanier–Whitehead dual of the space, and show that the map is an equivalence in the case where the space is a sphere. This results in a method for computing unstable vn-periodic homotopy groups of spheres from their Morava E-cohomology (as modules over the Dyer-Lashof algebra of Morava E-theory). We relate the resulting algebraic computations to the algebraic geometry of isogenies between Lubin–Tate formal groups.
AB - We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological André-Quillen cohomology of the K(n)-local Spanier–Whitehead dual of the space, and show that the map is an equivalence in the case where the space is a sphere. This results in a method for computing unstable vn-periodic homotopy groups of spheres from their Morava E-cohomology (as modules over the Dyer-Lashof algebra of Morava E-theory). We relate the resulting algebraic computations to the algebraic geometry of isogenies between Lubin–Tate formal groups.
UR - http://www.scopus.com/inward/record.url?scp=85077568692&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85077568692&partnerID=8YFLogxK
U2 - 10.1007/s00222-019-00941-x
DO - 10.1007/s00222-019-00941-x
M3 - Article
AN - SCOPUS:85077568692
SN - 0020-9910
VL - 220
SP - 949
EP - 1022
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -