2023/09/16 by Peng Du, Du, Peng, Alexander Vishik +1 · 1 citation
Computer Science · Mathematics · #14F42 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2309.09077
openalex publication_date 2023/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the Morava-isotropic stable homotopy category and, more generally, the stable homotopy category of an extension E/k. These "local" versions of the Morel-Voevodsky stable \BbbA1-homotopy category SH(k) are analogues of local motivic categories introduced in [22], but with a substantially more general notion of "isotropy". This permits to construct the, so-called, isotropic Morava points of the Balmer spectrum Spc(SHc(k)) of (the compact part of) the Morel-Voevodsky category. These analogues of topological Morava points are parametrized by the choice of Morava K-theory and a K(p,m)-equivalence class of extensions E/k. This provides a large supply of new points, and substantially improves our understanding of the spectrum. An interesting new feature is that the specialization among isotropic points behaves differently than in topology.