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.
Original language | English |
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Pages (from-to) | 3511-3564 |
Number of pages | 54 |
Journal | Geometry and Topology |
Volume | 28 |
Issue number | 8 |
DOIs | |
State | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2024 The Authors.
Keywords
- chromatic homotopy
- cyclotomic extensions
- Galois
- Picard