Picard groups of higher real -theory spectra at height

2015/11/25 by Drew Heard, Akhil Mathew, Vesna Stojanoska · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Descent (aeronautics) #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Picard group #Prime (order theory) #Sequence (biology) #Spectral line #Spectral sequence #math.AT

paper · pdf · doi:10.1112/s0010437x17007242

published as Compositio Math. 153 (2017) 1820-1854 · 33 pages, comments welcome

arxiv created 2015/11/25 · openalex created_date 2016/06/24 · openalex publication_date 2017/06/20 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05

Abstract

Using the descent spectral sequence for a Galois extension of ring spectra, we compute the Picard group of the higher real K -theory spectra of Hopkins and Miller at height n=p-1 , for p an odd prime. More generally, we determine the Picard groups of the homotopy fixed points spectra E_n^hG , where E_n is Lubin–Tate E -theory at the prime p and height n=p-1 , and G is any finite subgroup of the extended Morava stabilizer group. We find that these Picard groups are always cyclic, generated by the suspension.

Citations

• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
• Formal Groups

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