Chromatic cyclotomic extensions

Carmeli, Shachar¹ ; Schlank, Tomer M² ; Yanovski, Lior³

¹ Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
² Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
³ Max Planck Institute for Mathematics, Bonn, Germany, Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel

Geometry & topology, Tome 28 (2024) no. 8, pp. 3511-3564.

Résumé

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.

Détail

DOI : 10.2140/gt.2024.28.3511

Keywords: chromatic homotopy, cyclotomic extensions, Picard, Galois

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