Geodesic
Homological support of big objects in tensor-triangulated categories
[Support homologique des grands objets dans les catégories triangulées tensorielles]
Balmer, Paul1
1 Mathematics Department, UCLA, Los Angeles, CA 90095-1555, USA
Journal de l’École polytechnique — Mathématiques, Tome 7 (2020), pp. 1069-1088.

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Using homological residue fields, we define supports for big objects in tensor-triangulated categories and prove a tensor-product formula.

À l’aide des corps résiduels homologiques, nous définissons le support des grands objets dans les catégories triangulées tensorielles et prouvons une formule pour le support du produit tensoriel.

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DOI : 10.5802/jep.135
Classification : 18D99, 20J05, 55U35
Keywords: Tensor-triangular geometry, homological residue field, big support
Mots-clés : Géométrie triangulée-tensorielle, corps résiduels homologiques, support

Balmer, Paul 1

1 Mathematics Department, UCLA, Los Angeles, CA 90095-1555, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Balmer, Paul. Homological support of big objects in tensor-triangulated categories. Journal de l’École polytechnique — Mathématiques, Tome 7 (2020), pp. 1069-1088. doi : 10.5802/jep.135. http://geodesic.mathdoc.fr/articles/10.5802/jep.135/

[Bal05] Balmer, Paul The spectrum of prime ideals in tensor triangulated categories, J. reine angew. Math., Volume 588 (2005), pp. 149-168 | MR | Zbl | DOI

[Bal18] Balmer, Paul On the surjectivity of the map of spectra associated to a tensor-triangulated functor, Bull. London Math. Soc., Volume 50 (2018) no. 3, pp. 487-495 | MR | Zbl | DOI

[Bal19] Balmer, Paul A guide to tensor-triangular classification, Handbook of homotopy theory (Miller, H., ed.), Chapman and Hall/CRC, 2019 (Available on the author’s web page)

[Bal20] Balmer, Paul Nilpotence theorems via homological residue fields, Tunis. J. Math., Volume 2 (2020) no. 2, pp. 359-378 | Zbl | MR | DOI

[BC20] Balmer, Paul; Cameron, James Computing homological residue fields in algebra and topology, 2020 | arXiv

[BDS16] Balmer, Paul; Dell’Ambrogio, Ivo; Sanders, Beren Grothendieck-Neeman duality and the Wirthmüller isomorphism, Compositio Math., Volume 152 (2016) no. 8, pp. 1740-1776 | Zbl | DOI

[BF11] Balmer, Paul; Favi, Giordano Generalized tensor idempotents and the telescope conjecture, Proc. London Math. Soc. (3), Volume 102 (2011) no. 6, pp. 1161-1185 | MR | Zbl | DOI

[BIK08] Benson, David J.; Iyengar, Srikanth B.; Krause, Henning Local cohomology and support for triangulated categories, Ann. Sci. École Norm. Sup. (4), Volume 41 (2008) no. 4, pp. 573-619 | MR | mathdoc-id | Zbl | DOI

[BIK11a] Benson, David J.; Iyengar, Srikanth B.; Krause, Henning Stratifying modular representations of finite groups, Ann. of Math. (2), Volume 174 (2011) no. 3, pp. 1643-1684 | MR | Zbl | DOI

[BIK11b] Benson, David J.; Iyengar, Srikanth B.; Krause, Henning Stratifying triangulated categories, J. Topology, Volume 4 (2011) no. 3, pp. 641-666 | MR | Zbl | DOI

[BIK12a] Benson, David J.; Iyengar, Srikanth B.; Krause, Henning Colocalizing subcategories and cosupport, J. reine angew. Math., Volume 673 (2012), pp. 161-207 | MR | Zbl | DOI

[BIK12b] Benson, David J.; Iyengar, Srikanth B.; Krause, Henning Representations of finite groups: local cohomology and support, Oberwolfach Seminars, 43, Birkhäuser/Springer, Basel, 2012 | MR | Zbl | DOI

[BIK13] Benson, David J.; Iyengar, Srikanth B.; Krause, Henning Module categories for group algebras over commutative rings, J. K-Theory, Volume 11 (2013) no. 2, pp. 297-329 (With an appendix by Greg Stevenson) | MR | Zbl | DOI

[BKS19] Balmer, Paul; Krause, Henning; Stevenson, Greg Tensor-triangular fields: ruminations, Selecta Math. (N.S.), Volume 25 (2019) no. 1, 13, 36 pages | MR | Zbl | DOI

[BKS20] Balmer, Paul; Krause, Henning; Stevenson, Greg The frame of smashing tensor-ideals, Math. Proc. Cambridge Philos. Soc., Volume 168 (2020) no. 2, pp. 323-343 | MR | Zbl | DOI

[DP08] Dwyer, W. G.; Palmieri, J. H. The Bousfield lattice for truncated polynomial algebras, Homology Homotopy Appl., Volume 10 (2008) no. 1, pp. 413-436 | MR | Zbl | DOI

[HPS97] Hovey, Mark; Palmieri, John H.; Strickland, Neil P. Axiomatic stable homotopy theory, Mem. Amer. Math. Soc., 128, no. 610, American Mathematical Society, Providence, RI, 1997 | Zbl | DOI

[HS99] Hovey, Mark; Strickland, Neil P. Morava K-theories and localisation, Mem. Amer. Math. Soc., 139, no. 666, American Mathematical Society, Providence, RI, 1999 | Zbl | DOI

[Kra00] Krause, Henning Smashing subcategories and the telescope conjecture—an algebraic approach, Invent. Math., Volume 139 (2000) no. 1, pp. 99-133 | MR | Zbl | DOI

[Lur17] Lurie, Jacob Higher algebra (2017) (Online at http://www.math.ias.edu/~lurie/)

[Nee96] Neeman, Amnon The Grothendieck duality theorem via Bousfield’s techniques and Brown representability, J. Amer. Math. Soc., Volume 9 (1996) no. 1, pp. 205-236 | MR | Zbl | DOI

[Nee00] Neeman, Amnon Oddball Bousfield classes, Topology, Volume 39 (2000) no. 5, pp. 931-935 | MR | Zbl | DOI

[Nee01] Neeman, Amnon Triangulated categories, Annals of Math. Studies, 148, Princeton University Press, Princeton, NJ, 2001 | MR | Zbl | DOI

[Ste13] Stevenson, Greg Support theory via actions of tensor triangulated categories, J. reine angew. Math., Volume 681 (2013), pp. 219-254 | MR | Zbl | DOI

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