scholarly journals Homological support of big objects in tensor-triangulated categories

2020 ◽  
Vol 7 ◽  
pp. 1069-1088
Author(s):  
Paul Balmer
Keyword(s):  
Triangulated Categories ◽  
Tensor Triangulated Categories

scholarly journals Adelic models of tensor-triangulated categories

2020 ◽  
Vol 375 ◽  
pp. 107339 ◽  
Author(s):  
Scott Balchin ◽  
J.P.C. Greenlees
Keyword(s):  
Triangulated Categories ◽  
Tensor Triangulated Categories

scholarly journals Affine weakly regular tensor triangulated categories

2016 ◽  
Vol 285 (1) ◽  
pp. 93-109 ◽  
Author(s):  
Ivo Dell’Ambrogio ◽  
Donald Stanley
Keyword(s):  
Triangulated Categories ◽  
Tensor Triangulated Categories

Perfect complexes on Deligne-Mumford stacks and applications

2009 ◽  
Vol 4 (3) ◽  
pp. 559-603 ◽  
Author(s):  
Amalendu Krishna
Keyword(s):  
Full Subcategory ◽  
Derived Categories ◽  
Derived Category ◽  
Triangulated Categories ◽  
Localization Theorem ◽  
Coherent Sheaves ◽  
Perfect Complexes ◽  
Tensor Triangulated Categories ◽  
Resolution Property

AbstractFor a tame Deligne-Mumford stack X with the resolution property, we show that the Cartan-Eilenberg resolutions of unbounded complexes of quasicoherent sheaves are K-injective resolutions. This allows us to realize the derived category of quasi-coherent sheaves on X as a reflexive full subcategory of the derived category of X-modules.We then use the results of Neeman and recent results of Kresch to establish the localization theorem of Thomason-Trobaugh for the K-theory of perfect complexes on stacks of above type which have coarse moduli schemes. As a byproduct, we get a generalization of Krause's result about the stable derived categories of schemes to such stacks.We prove Thomason's classification of thick triangulated tensor subcategories of D(perf / X). As the final application of our localization theorem, we show that the spectrum of D(perf / X) as defined by Balmer, is naturally isomorphic to the coarse moduli scheme of X, answering a question of Balmer for the tensor triangulated categories arising from Deligne-Mumford stacks.

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