Chromatic Cyclotomic Extensions

Abstract

We construct Galois extensions of the T(n)-local sphere, lifting all finite abelian Galois extensions of the K(n)-local sphere. This is achieved by realizing them as higher semiadditive analogues of cyclotomic extensions. Combining this with a general form of Kummer theory, we lift certain elements from the K(n)-local Picard group to the T(n)-local Picard group.

53 pages. Edited in response to comments of the referee. Fixed typos, some arguments expanded and made more precise, added details in section 5.2. Accepted to GnT

References in corpus (3)

• The linearity of traces in monoidal categories and bicategories
• Purity in chromatically localized algebraic $K$-theory
• Adjoining roots in homotopy theory

Cited by in corpus (5)

• Higher semiadditive Grothendieck-Witt theory and the $K(1)$-local sphere
• Characters and transfer maps via categorified traces
• On the parametrized Tate construction
• On the Non-Existence of J-Homomorphisms of Higher Height
• The inverse limit topology and profinite descent on Picard groups in $K(n)$-local homotopy theory