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tt-geometry of Tate motives over algebraically closed fields

Part of: Categories with structure Cycles and subschemes Homological algebra (Co)homology theory $K$-theory in geometry Abelian categories

Published online by Cambridge University Press:  06 September 2019

Martin Gallauer
Martin Gallauer*
Affiliation:
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK URL: http://people.maths.ox.ac.uk/gallauer email [email protected]
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Abstract

We study Tate motives with integral coefficients through the lens of tensor triangular geometry. For some base fields, including $\overline{\mathbb{Q}}$ and $\overline{\mathbb{F}_{p}}$, we arrive at a complete description of the tensor triangular spectrum and a classification of the thick tensor ideals.

Keywords

tt-geometrymotiveTate motiveclassificationcohomology

MSC classification

Primary: 14C15: (Equivariant) Chow groups and rings; motives 14F42: Motivic cohomology; motivic homotopy theory 19E15: Algebraic cycles and motivic cohomology 18E30: Derived categories, triangulated categories 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories 18G99: None of the above, but in this section
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 10 , October 2019 , pp. 1888 - 1923
Copyright
© The Author 2019 

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