Real orientations of Lubin-Tate spectra

• 成果类型: Article
• 署名作者: Hahn, Jeremy; Shi, XiaoLin Danny
• 署名单位: Massachusetts Institute of Technology (MIT); University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00960-z
• 发表日期: 2020
• 页码: 731-776
• 关键词: kervaire invariant; homotopy-theory; K-THEORY; ELEMENTS; nonexistence; MANIFOLDS; analog

摘要

We show that Lubin-Tate spectra at the prime 2 are Real oriented and Real Landweber exact. The proof is by application of the Goerss-Hopkins-Miller theorem to algebras with involution. For each height n, we compute the entire homotopy fixed point spectral sequence for E-n with its C-2-action given by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these C-2-fixed points.