2020/04/30 by Herman Rohrbach · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Base (topology) #Bundle #Computer science #Grothendieck group #Hermitian matrix #Homotopy and Cohomology in Algebraic Topology #Line bundle #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Resolution (logic) #Scheme (mathematics) #Spectral line #Spectrum (functional analysis) #Witt vector #math.AG #math.KT
paper · pdf · doi:10.1016/j.jpaa.2021.106917
published in Journal of Pure and Applied Algebra 226(5), 106917 (Elsevier BV) · 20 pages
arxiv created 2020/09/08 · openalex publication_date 2021/09/29 · arxiv updated 2022/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Grothendieck-Witt spectra represent higher Grothendieck-Witt groups and higher Hermitian K-theory in particular. A description of the Grothendieck-Witt spectrum of a finite dimensional projective bundle ℙ(E) over a base scheme X is given in terms of the Grothendieck-Witt spectra of the base, using the dg category of strictly perfect complexes, provided that X is a scheme over Spec ℤ[1/2] and satisfies the resolution property, e.g. if X has an ample family of line bundles.