TY - JOUR
T1 - Chromatic Cardinalities via Redshift
AU - Ben-Moshe, Shay
AU - Carmeli, Shachar
AU - Schlank, Tomer M.
AU - Yanovski, Lior
N1 - Publisher Copyright:
© The Author(s) 2024. Published by Oxford University Press.
PY - 2024/7/1
Y1 - 2024/7/1
N2 - Using higher descent for chromatically localized algebraic K-theory, we show that the higher semiadditive cardinality of a π-finite p-space A at the Lubin–Tate spectrum En is equal to the higher semiadditive cardinality of the free loop space LA at En−1. By induction, it is thus equal to the homotopy cardinality of the n-fold free loop space LnA. We explain how this allows one to bypass the Ravenel–Wilson computation in the proof of the ∞-semi-additivity of the T(n)-local categories.
AB - Using higher descent for chromatically localized algebraic K-theory, we show that the higher semiadditive cardinality of a π-finite p-space A at the Lubin–Tate spectrum En is equal to the higher semiadditive cardinality of the free loop space LA at En−1. By induction, it is thus equal to the homotopy cardinality of the n-fold free loop space LnA. We explain how this allows one to bypass the Ravenel–Wilson computation in the proof of the ∞-semi-additivity of the T(n)-local categories.
UR - http://www.scopus.com/inward/record.url?scp=85199357738&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnae109
DO - 10.1093/imrn/rnae109
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AN - SCOPUS:85199357738
SN - 1073-7928
VL - 2024
SP - 10918
EP - 10924
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 14
ER -