Volume 22, issue 4 (2018)

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Primes and fields in stable motivic homotopy theory

Jeremiah Heller and Kyle M Ormsby

Geometry & Topology 22 (2018) 2187–2218

Let F be a field of characteristic different from 2. We establish surjectivity of Balmer’s comparison map

ρ: Spc(SHA1 (F)c) Spech(K MW(F))

from the tensor triangular spectrum of the homotopy category of compact motivic spectra to the homogeneous Zariski spectrum of Milnor–Witt K–theory. We also comment on the tensor triangular geometry of compact cellular motivic spectra, producing in particular novel field spectra in this category. We conclude with a list of questions about the structure of the tensor triangular spectrum of the stable motivic homotopy category.

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tensor triangular geometry, stable motivic homotopy theory
Mathematical Subject Classification 2010
Primary: 14F42
Secondary: 19D45, 55P42, 18E30
Received: 19 August 2016
Revised: 19 July 2017
Accepted: 29 August 2017
Published: 5 April 2018
Proposed: Stefan Schwede
Seconded: Mark Behrens, Haynes R Miller
Jeremiah Heller
Department of Mathematics
University of Illinois at Urbana-Champaign
United States
Kyle M Ormsby
Department of Mathematics
Reed College
United States