Publikace · Jan Šťovíček

Články a preprinty

1. All n-cotilting modules are pure-injective, Proc. Amer. Math. Soc. 134 (2006), 1891-1897, doi:10.1090/S0002-9939-06-08256-6. [link to the journal]
2. (with Jan Trlifaj): All tilting modules are of countable type, Bull. Lond. Math. Soc. 39 (2007), 121-132, doi:10.1112/blms/bdl019. [link to the journal]
3. (with Silvana Bazzoni): All tilting modules are of finite type, Proc. Amer. Math. Soc. 135 (2007), 3771-3781, doi:10.1090/S0002-9939-07-08911-3. [link to the journal]
4. Tilting modules over an algebra by Igusa, Smalø and Todorov, Journal of Algebra 311 (2007) 299-318, doi:10.1016/j.jalgebra.2006.11.017. [link to the journal] [PDF file - accepted author's manuscript]
5. (with Jan Trlifaj): Generalized Hill lemma, Kaplansky theorem for cotorsion pairs, and some applications, Rocky Mountain J. Math. 39 (2009), no. 1, 305-324, doi:10.1216/rmj-2009-39-1-305. [link to the journal] [PDF file - preprint]
6. (with Silvana Bazzoni): Sigma-cotorsion modules over valuation domains, Forum Math. 21 (2009), no. 5, 893–920, doi:10.1515/forum.2009.044. [link to the journal] [PDF file - preprint]
7. (with Jan Saroch): The countable telescope conjecture for module categories, Adv. Math. 219 (2008), 1002-1036, doi:10.1016/j.aim.2008.05.012. [link to the journal] [arXiv:0801.3936]
8. Telescope conjecture, idempotent ideals, and the transfinite radical, Trans. Amer. Math. Soc. 362 (2010), 1475-1489, doi:10.1090/s0002-9947-09-04812-0. [link to the journal] [arXiv:0802.2189]
9. (with Henning Krause): The telescope conjecture for hereditary rings via Ext-orthogonal pairs, Adv. Math. 225 (2010), 2341-2364, doi:10.1016/j.aim.2010.04.027. [link to the journal] [arXiv:0810.1401]
10. Locally well generated homotopy categories of complexes, Doc. Math. 15 (2010), 507-525. [link to the journal] [arXiv:0810.5684]
11. (with Otto Kerner and Jan Trlifaj): Tilting via torsion pairs and almost hereditary noetherian rings, J. Pure Appl. Algebra 215 (2011), 2072-2085, doi:10.1016/j.jpaa.2010.11.016. [link to the journal] [arXiv:0903.5454]
12. A characterization of long exact sequences coming from the snake lemma, Math. Res. Lett. 17 (2010), 147-156, doi:10.4310/MRL.2010.v17.n1.a11. [link to the journal] [arXiv:0906.1286]
13. (with Manuel Saorín): On exact categories and applications to triangulated adjoints and model structures, Adv. Math. 228 (2011), 968-1007, doi:10.1016/j.aim.2011.05.025. [link to the journal] [arXiv:1005.3248]
14. Deconstructibility and the Hill lemma in Grothendieck categories, Forum Math. 25 (2013), no. 1, 193-219, doi:10.1515/FORM.2011.113. [link to the journal] [arXiv:1005.3251]
15. (with Steffen Oppermann): Generating the bounded derived category and perfect ghosts, Bull. London Math. Soc. 44 (2012), 285-298, doi:10.1112/blms/bdr093. [link to the journal] [arXiv:1006.3568]
16. (with Silvana Bazzoni): Flat Mittag-Leffler modules over countable rings, Proc. Amer. Math. Soc. 140 (2012), 1527-1533, doi:10.1090/S0002-9939-2011-11070-0. [link to the journal] [arXiv:1007.4977]
17. (with George Ciprian Modoi) Brown representability often fails for homotopy categories of complexes, J. K-Theory 9 (2012), 151–160, doi:10.1017/is011010026jkt167. [link to the journal] [arXiv:1012.4109]
18. (with Silvana Bazzoni): On the abelianization of derived categories and a negative solution to Rosický's problem, Compos. Math. 149 (2013), 125-147, doi:10.1112/S0010437X12000413. [link to the journal] [arXiv:1102.3240]
19. (with Lidia Angeleri Hügel, David Pospisil and Jan Trlifaj): Tilting, cotilting, and spectra of commutative noetherian rings, Trans. Amer. Math. Soc. 366 (2014), 3487-3517, doi:10.1090/S0002-9947-2014-05904-7. [link to the journal] [arXiv:1203.0907]
20. (with Joanne L. Hall): Mutually unbiased bases as submodules and subspaces, Proceedings of the 2012 IEEE International Symposium on Information Theory, ISIT 2012, Cambridge, MA, USA, 905-909, doi:10.1109/ISIT.2012.6284693. [link to the publisher] [arXiv:1206.0531]
21. (with David Pospisil): On compactly generated torsion pairs and the classification of co-t-structures for commutative noetherian rings, Trans. Amer. Math. Soc. 368 (2016), 6325-6361, doi:10.1090/tran/6561. [link to the journal] [arXiv:1212.3122]
22. Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves, in Advances in Representation Theory of Algebras (ICRA Bielefeld, Germany, 8-17 August, 2012), EMS Series of Congress Reports, European Mathematical Society Publishing House, doi:10.4171/125-1/10. [link to the publisher] [arXiv:1301.5206]
23. (with Dolors Herbera and Jan Trlifaj): Cotilting modules over commutative noetherian rings, J. Pure Appl. Algebra 218 (2014), 1696-1711, doi:10.1016/j.jpaa.2014.01.008. [link to the journal] [arXiv:1306.6788]
24. Derived equivalences induced by big cotilting modules, Adv. Math. 263 (2014), 45-87, doi:10.1016/j.aim.2014.06.007. [link to the journal] [arXiv:1308.1804]
25. (with Moritz Groth): Tilting theory via stable homotopy theory, J. reine angew. Math. 743 (2018), 29-90, doi:10.1515/crelle-2015-0092. [link to the journal] [arXiv:1401.6451]
26. (with Moritz Groth): Tilting theory for trees via stable homotopy theory, J. Pure Appl. Algebra 220 (2016), 2324-2363, doi:10.1016/j.jpaa.2015.11.009. [link to the journal] [arXiv:1402.6984]
27. (with Silvana Bazzoni): Smashing localizations of rings of weak global dimension at most one, Adv. Math. 305 (2017), 351-401, doi:10.1016/j.aim.2016.09.028. [link to the journal] [arXiv:1402.7294]
28. (with Moritz Groth): Abstract representation theory of Dynkin quivers of type A, Adv. Math. 293 (2016), 856-941, doi:10.1016/j.aim.2016.02.018. [link to the journal] [arXiv:1409.5003]
29. On purity and applications to coderived and singularity categories, preprint. [arXiv:1412.1615]
30. (with Frederik Marks): Torsion classes, wide subcategories and localisations, Bull. Lond. Math. Soc. 49 (2017), 405-416, doi:10.1112/blms.12033. [link to the journal] [arXiv:1503.04639]
31. (with Ivo Dell'Ambrogio and Greg Stevenson): Gorenstein homological algebra and universal coefficient theorems, Math. Z. 287 (2017), no. 3-4, 1109-1155, doi:10.1007/s00209-017-1862-7. [link to the journal] [arXiv:1510.00426]
32. (with Moritz Groth): Abstract tilting theory for quivers and related categories, Ann. K-Theory 3 (2018), no. 1, 71-124, doi:10.2140/akt.2018.3.71. [link to the journal] [arXiv:1512.06267]
33. (with Frederik Marks): Universal localisations via silting, Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), no. 2, 511-532, doi:10.1017/prm.2018.37. [link to the journal] [arXiv:1605.04222]
34. (with Adam-Christiaan van Roosmalen): 2-Calabi-Yau categories with a directed cluster-tilting subcategory, preprint. [arXiv:1611.03836]
35. (with Michal Hrbek): Tilting classes over commutative rings, Forum Math. 32 (2020), no. 1, doi:10.1515/forum-2017-0219. [link to the journal] [arXiv:1701.05534]
36. (with Pavel Coupek): Cotilting sheaves on Noetherian schemes, Math. Z. 296 (2020), no. 1-2, 275-312, doi:10.1007/s00209-019-02404-8. [link to the journal] [arXiv:1707.01677]
37. (with Manuel Saorín and Simone Virili): t-Structures on stable derivators and Grothendieck hearts, Adv. Math. 429 (2023), paper no. 109139, 70 pp., doi:10.1016/j.aim.2023.109139. [link to the journal] [arXiv:1708.07540]
38. (with Ivo Dell'Ambrogio): Mackey algebras which are Gorenstein, Algebr. Represent. Theory 23 (2020), no. 2, 281-284, doi:10.1007/s10468-018-09848-2. [link to the journal] [arXiv:1709.02146]
39. (with Leonid Positselski): The tilting-cotilting correspondence, Int. Math. Res. Not. IMRN 2021, no. 1, 191-276, doi:10.1093/imrn/rnz116. [link to the journal] [arXiv:1710.02230]
40. (with Leonid Positselski): Infinity-tilting theory, Pacific J. Math. 301 (2019), no. 1, 297-334, doi:10.2140/pjm.2019.301.297. [link to the journal] [arXiv:1711.06169]
41. (with Michal Hrbek and Jan Trlifaj): Zariski locality of quasi-coherent sheaves associated with tilting, Indiana Univ. Math. J. 69 (2020), no. 5, 1733-1762, doi:10.1512/iumj.2020.69.7987. [link to the journal] [arXiv:1712.08899]
42. (with Réamonn Ó Buachalla and Adam-Christiaan van Roosmalen): A Kodaira Vanishing Theorem for Noncommutative Kahler Structures, preprint. [arXiv:1801.08125]
43. (with Jan Saroch): Singular compactness and definability for Sigma-cotorsion and Gorenstein modules, Selecta Math. (N.S.) 26 (2020), paper no. 23, 40pp., doi: 10.1007/s00029-020-0543-2. [link to the journal] [arXiv:1804.09080]
44. (with Leonid Positselski): Exactness of direct limits for abelian categories with an injective cogenerator, J. Pure Appl. Algebra 223 (2019), 3330-3340, doi:10.1016/j.jpaa.2018.11.004. [link to the journal] [arXiv:1805.05156]
45. (with Lidia Angeleri Hügel, Frederik Marks, Ryo Takahashi and Jorge Vitória): Flat ring epimorphisms and universal localisations of commutative rings, Q. J. Math. 71 (2020), no. 4, 1489-1520, doi:10.1093/qmath/haaa041. [link to the journal] [arXiv:1807.01982]
46. (with Alexander Slavik): On flat generators and Matlis duality for quasicoherent sheaves, Bull. Lond. Math. Soc. 53 (2021), no. 1, 63-74, doi:10.1112/blms.12398. [link to the journal] [arXiv:1902.05740]
47. (with Leonid Positselski): Topologically semisimple and topologically perfect topological rings, Publ. Mat. 66 (2022), no. 2, 457-540, doi:10.5565/PUBLMAT6622202. [link to the journal] [arXiv:1909.12203]
48. (with Silvana Bazzoni and Leonid Positselski): Projective covers of flat contramodules, Int. Math. Res. Not. IMRN 2022, no. 24, 19527-19564, doi:10.1093/imrn/rnab202. [link to the journal] [arXiv:1911.11720]
49. (with Manuel Saorín): t-Structures with Grothendieck hearts via functor categories, Selecta Math. (N.S.) 29 (2023), paper no. 77, 73pp., doi:10.1007/s00029-023-00872-9. [link to the journal] [arXiv:2003.01401]
50. (with Leonid Positselski): Derived, coderived, and contraderived categories of locally presentable abelian categories, J. Pure Appl. Algebra 226 (2022), doi:10.1016/j.jpaa.2021.106883. [link to the journal] [arXiv:2101.10797]
51. (with Lidia Angeleri Hügel, Rosanna Laking and Jorge Vitória): Mutation and torsion pairs, preprint. [arXiv:2201.02147]
52. (with Leonid Positselski): Topologically semiperfect topological rings, Algebr. Represent. Theory 27 (2024), 245-278, doi:10.1007/s10468-023-10217-x. [link to the journal] [arXiv:2201.03488]
53. (with Michal Hrbek and Tsutomu Nakamura): Tilting complexes and codimension functions over commutative noetherian rings, Nagoya Math. J., published on-line, doi:10.1017/nmj.2024.1. [link to the journal] [arXiv:2207.01309]
54. (with Jakub Kopřiva): Semiorthogonal decompositions for bounded derived categories of gentle algebras, preprint. [arXiv:2209.14496]
55. (with Leonid Positselski): Coderived and contraderived categories of locally presentable abelian DG-categories, Math. Z., published on-line, doi:10.1007/s00209-024-03519-3. [link to the journal] [arXiv:2210.08237]
56. (with Leonid Positselski): Flat quasi-coherent sheaves as direct limits, and quasi-coherent cotorsion periodicity, preprint. [arXiv:2212.09639]
57. (with Leonid Positselski): Contraderived categories of CDG-modules, preprint. [arXiv:2401.07021]
58. (with Georgios Dalezios): Linear Reedy categories, quasi-hereditary algebras and model structures, preprint.

Knihy

• (with Jan Trlifaj, as editors): Representation theory and beyond, Workshop and 18th International Conference on Representations of Algebras (ICRA 2018), August 8-17, 2018, Prague, Czech Republic. Contemp. Math. 758, AMS, 2020, doi:10.1090/conm/758. [link to the publisher]

Práce (diplomová a disertační)

• Finitistic Dimensions of Rings, Charles University in Prague, Faculty of Mathematics and Physics, 2004. [PDF file]
• Artin Algebras and Infinitely Generated Tilting Modules, Charles University in Prague, Faculty of Mathematics and Physics, 2008. [PDF file]
• Compactly Generated Triangulated Categories and the Telescope Conjecture, Norwegian University of Science and Technology, 2009. [PDF file]

Prezentace z přednášek

Na konferencích a seminářích většinou přednáším s pomocí tabule. Níže uvádím pouze moje prezentace v Beameru, proto není seznam úplně reprezentativní.

• Ext and vanishing of derived functors of inverse limits, talk given at the Second Czech-Catalan Conference in Mathematics in Barcelona, Spain in 2006. [PDF file]
• Idempotent ideals in a module category and the Telescope conjecture, talk given at ICRA XII in Torun, Poland in 2007. [PDF file]
• Axioms, algorithms and Hilbert’s Entscheidungsproblem, talk given in a student seminar in Trondheim, Norway in 2008. [PDF file]
• Categorification—the sl₂ case (functor valued invariants of knots, links and tangles), trial lecture for the Ph.D. defense in Trondheim, Norway in 2009. [PDF file]
• Tilting modules—homological algebra and structure, talk given at the Joint Mathematical Conference CSASC 2010 in Prague, Czech Republic in 2010. [PDF file]
• A counterexample to Rosicky's problem, talk given at the ECC Workshop on Categories, Algebras and Representations in Prague, Czech Republic in 2010. [PDF file]
• Infinite combinatorics in homological algebra, talk given at the Advanced Course and Workshop on Large-Cardinal Methods in Homotopy in Barcelona, Spain in 2011. [PDF file]
• Generating the bounded derived category and perfect ghosts, talk given at the ÖMG-Tagung CSASC 2011 at Donauuniversität Krems in Austria. [PDF file]
• Derived categories with a view towards Grothendieck duality, talk given at the ECC meeting in Telc, Czech Republic in 2011. [PDF file]
• Localizations of the derived category of a valuation domain, talk given at the ECI Workshop on Categories, Algebras and Representations in Prague, Czech Republic in 2012. [PDF file]
• Abstract representation theory using Grothendieck derivators, talk given at the AMeGA+ECI Workshop in Třešť, Czech Republic in 2014. [PDF file]
• Smashing localization for rings of weak global dimension 1, talk given at Algebraic Structures and Their Applications in Spineto, Italy in 2014. [PDF file]
• Tilting theory in the context of Grothendieck derivators, talk given in the special session Rings, Modules, Categories and Applications at the First Joint International Meeting of RSME-SCM-SEMA-SIMAI-UMI in Bilbao, Spain in 2014. [PDF file]
• Representability of functors and Gorenstein homological algebra, talk given at the ECI Workshop in Třešť, Czech Republic in 2015. [PDF file]
• Derived equivalences induced by big tilting modules, talk given in the session Applications of categories in algebra and topology of CSASC 2016 in Barcelona, Spain, 2016. [PDF file]
• Flat epimorphisms of commutative noetherian rings, talk given in the workshop Categorical Methods in Algebra and Topology at CSASC 2018 in Bratislava, Slovakia, 2018. [PDF file]
• Noncommutative algebraic geometry based on quantum flag manifolds, three lectures given at 39th Winter School Geometry and Physics in Srni, Czech Republic, 2019. [PDF file, lecture 1] [PDF file, lecture 2] [PDF file, lecture 3] [PDF file, all lectures]
• The smashing spectrum of a valuation domain, on-line talk given a the JTP seminar series Non-commutative motives and telescope-type problems given at the Hausdorff Research Institute for Mathematics, Bonn, Germany, 2020. [PDF file]
• On the Finitistic Dimension Conjecture, on-line talk given at İzmir Mathematical Days 2022, Turkey, 2022. [PDF file]