Algebraic & Geometric Topology Volume 22, issue 6 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Torsion models for tensor-triangulated categories: the one-step case

Scott Balchin, John Greenlees, Luca Pol and Jordan Williamson

Algebraic & Geometric Topology 22 (2022) 2805–2856

DOI: 10.2140/agt.2022.22.2805

Bibliography

1	M M Abbasirad, Homotopy theory of differential graded modules and adjoints of restriction of scalars, PhD thesis, University of Sheffield (2014) MR3389527
2	S Balchin, T Barthel, J P C Greenlees, Prismatic decompositions and rational G–spectra, in preparation
3	S Balchin, J P C Greenlees, Adelic models of tensor-triangulated categories, Adv. Math. 375 (2020) 107339, 45 MR4135418
4	S Balchin, J P C Greenlees, L Pol, J Williamson, Torsion models for tensor-triangulated categories, in preparation
5	P Balmer, The spectrum of prime ideals in tensor triangulated categories, J. Reine Angew. Math. 588 (2005) 149 MR2196732
6	P Balmer, Supports and filtrations in algebraic geometry and modular representation theory, Amer. J. Math. 129 (2007) 1227 MR2354319
7	P Balmer, G Favi, Generalized tensor idempotents and the telescope conjecture, Proc. Lond. Math. Soc. 102 (2011) 1161 MR2806103
8	D Barnes, Splitting monoidal stable model categories, J. Pure Appl. Algebra 213 (2009) 846 MR2494375
9	D Barnes, J P C Greenlees, M Kędziorek, B Shipley, Rational SO(2)–equivariant spectra, Algebr. Geom. Topol. 17 (2017) 983 MR3623679
10	T Barthel, D Heard, G Valenzuela, Local duality in algebra and topology, Adv. Math. 335 (2018) 563 MR3836674
11	D Benson, S B Iyengar, H Krause, Local cohomology and support for triangulated categories, Ann. Sci. Éc. Norm. Supér. 41 (2008) 573 MR2489634
12	J E Bergner, Homotopy limits of model categories and more general homotopy theories, Bull. Lond. Math. Soc. 44 (2012) 311 MR2914609
13	M P Brodmann, R Y Sharp, Local cohomology: An algebraic introduction with geometric applications, 136, Cambridge Univ. Press (2013) MR3014449
14	M Brun, B I Dundas, M Stolz, Equivariant structure on smash powers, preprint (2016) arXiv:1604.05939
15	A B Buan, H Krause, Ø Solberg, Support varieties: an ideal approach, Homology Homotopy Appl. 9 (2007) 45 MR2280286
16	D Dugger, Replacing model categories with simplicial ones, Trans. Amer. Math. Soc. 353 (2001) 5003 MR1852091
17	W G Dwyer, J P C Greenlees, Complete modules and torsion modules, Amer. J. Math. 124 (2002) 199 MR1879003
18	J P C Greenlees, Rational S¹–equivariant stable homotopy theory, 661, Amer. Math. Soc. (1999) MR1483831
19	J P C Greenlees, Tate cohomology in axiomatic stable homotopy theory, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 149 MR1851253
20	J P C Greenlees, The Balmer spectrum of rational equivariant cohomology theories, J. Pure Appl. Algebra 223 (2019) 2845 MR3912951
21	J P C Greenlees, Couniversal spaces which are equivariantly commutative ring spectra, Homology Homotopy Appl. 22 (2020) 69 MR4027290
22	J P C Greenlees, J P May, Completions in algebra and topology, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 255 MR1361892
23	J P C Greenlees, B Shipley, An algebraic model for free rational G–spectra for connected compact Lie groups G, Math. Z. 269 (2011) 373 MR2836075
24	J P C Greenlees, B Shipley, The cellularization principle for Quillen adjunctions, Homology Homotopy Appl. 15 (2013) 173 MR3138375
25	J P C Greenlees, B Shipley, Fixed point adjunctions for equivariant module spectra, Algebr. Geom. Topol. 14 (2014) 1779 MR3212584
26	J P C Greenlees, B Shipley, Homotopy theory of modules over diagrams of rings, Proc. Amer. Math. Soc. Ser. B 1 (2014) 89 MR3254575
27	J P C Greenlees, B Shipley, An algebraic model for rational torus-equivariant spectra, J. Topol. 11 (2018) 666 MR3830880
28	T Haraguchi, On model structure for coreflective subcategories of a model category, Math. J. Okayama Univ. 57 (2015) 79 MR3289294
29	K Hess, M Kȩdziorek, E Riehl, B Shipley, A necessary and sufficient condition for induced model structures, J. Topol. 10 (2017) 324 MR3653314
30	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
31	M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, II, Ann. of Math. 148 (1998) 1 MR1652975
32	M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
33	M Hovey, J H Palmieri, N P Strickland, Axiomatic stable homotopy theory, 610, Amer. Math. Soc. (1997) MR1388895
34	L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
35	S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. 80 (2000) 491 MR1734325
36	S Schwede, B Shipley, Equivalences of monoidal model categories, Algebr. Geom. Topol. 3 (2003) 287 MR1997322
37	B Shipley, A convenient model category for commutative ring spectra, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 473 MR2066511
38	B Shipley, Hℤ–algebra spectra are differential graded algebras, Amer. J. Math. 129 (2007) 351 MR2306038
39	G Stevenson, Support theory via actions of tensor triangulated categories, J. Reine Angew. Math. 681 (2013) 219 MR3181496
40	G Stevenson, Filtrations via tensor actions, Int. Math. Res. Not. 2018 (2018) 2535 MR3801492
41	G Stevenson, A tour of support theory for triangulated categories through tensor triangular geometry, from: "Building bridges between algebra and topology" (editors D Herbera, W Pitsch, S Zarzuela), Springer (2018) 63 MR3793858
42	B Toën, G Vezzosi, Homotopical algebraic geometry, II : Geometric stacks and applications, 902, Amer. Math. Soc. (2008) MR2394633
43	D White, Model structures on commutative monoids in general model categories, J. Pure Appl. Algebra 221 (2017) 3124 MR3666740
44	D White, Monoidal Bousfield localizations and algebras over operads, from: "Equivariant topology and derived algebra" (editors S Balchin, D Barnes, M Kędziorek, M Szymik), London Math. Soc. Lecture Note Ser. 474, Cambridge Univ. Press (2022) 180 MR4327101
45	J Williamson, Flatness and Shipley’s algebraicization theorem, Homology Homotopy Appl. 23 (2021) 191 MR4146001
46	J Williamson, Algebraic models of change of groups functors in (co)free rational equivariant spectra, J. Pure Appl. Algebra 226 (2022) MR4414841