tensor triangulated category
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2018 ◽  
Vol 168 (2) ◽  
pp. 323-343 ◽  
Author(s):  
PAUL BALMER ◽  
HENNING KRAUSE ◽  
GREG STEVENSON

AbstractWe prove that every flat tensor-idempotent in the module category Mod- of a tensor-triangulated category comes from a unique smashing ideal in . We deduce that the lattice of smashing ideals forms a frame.


2018 ◽  
Vol 2018 (738) ◽  
pp. 237-280 ◽  
Author(s):  
Amnon Neeman

AbstractSuppose{({\mathscr{T}},\otimes,\mathds{1})}is a tensor triangulated category. In a number of recent articles Balmer defines and explores the notion of “separable tt-rings” in{{\mathscr{T}}}(in this paper we will call them “separable monoids”). The main result of this article is that, if{{\mathscr{T}}}is the derived quasicoherent category of a noetherian schemeX, then the only separable monoids are the pushforwards by étale maps of smashing Bousfield localizations of the structure sheaf.


2012 ◽  
Vol 11 (3) ◽  
pp. 611-657 ◽  
Author(s):  
Amalendu Krishna ◽  
Jinhyun Park

AbstractFor a perfect field k, we use the techniques of Bondal-Kapranov and Hanamura to construct a tensor triangulated category of mixed motives over the truncated polynomial ring k[t]/(tm+1). The extension groups in this category are given by Bloch's higher Chow groups and the additive higher Chow groups. The main new ingredient is the moving lemma for additive higher Chow groups by the authors and its refinements.


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