L. Positselski - Publications

2024

Positselski L., Šťovíček J., Contraderived categories of CDG-modules. Electronic preprint arXiv:2401.07021 [math.RA], 66 pp. http://iitp.ru/https://arxiv.org/abs/2401.07021

Positselski L., The categories of corings and coalgebras over a ring are locally countably presentable. Electronic preprint arXiv:2401.02928 [math.RA], 21 pp. http://iitp.ru/https://arxiv.org/abs/2401.02928

Positselski L., Philosophy of contraherent cosheaves. Electronic preprint arXiv:2311.14179 [math.AG], 65 pp. http://iitp.ru/https://arxiv.org/abs/2311.14179

Positselski L., Locally coherent exact categories. Electronic preprint arXiv:2311.02418 [math.CT], 33 pp. http://iitp.ru/https://arxiv.org/abs/2311.02418

Positselski L., A bounded below, noncontractible, acyclic complex of projective modules. Acta Math. Hungarica, published online in March 2024, DOI:10.1007/s10474-024-01414-1, 22 pp. http://iitp.ru/https://arxiv.org/abs/2305.11119

Positselski L., Generalized periodicity theorems. Electronic preprint arXiv:2301.00708 [math.RA], 38 pp. http://iitp.ru/https://arxiv.org/abs/2301.00708

Positselski L., Local, colocal, and antilocal properties of modules and complexes over commutative rings. Journ. of Algebra 646 (2024), p.100-155. http://iitp.ru/https://arxiv.org/abs/2212.10163

Positselski L., Šťovíček J., Topologically semiperfect topological rings. Algebras and Represent. Theory 27 (2024), #1, p.245-278. http://iitp.ru/https://arxiv.org/abs/2201.03488

2023

Positselski L., Resolutions as directed colimits. Electronic preprint arXiv:2312.07197 [math.AC], 37 pp. http://iitp.ru/https://arxiv.org/abs/2312.07197

Positselski L., Notes on limits of accessible categories. Electronic preprint arXiv:2310.16773 [math.CT], 35 pp. http://iitp.ru/https://arxiv.org/abs/2310.16773

Positselski L., Semialgebras associated with nonunital algebras and k-linear subcategories. Electronic preprint arXiv:2310.05550 [math.CT], 60 pp. http://iitp.ru/https://arxiv.org/abs/2310.05550

Positselski L., Tensor-Hom formalism for modules over nonunital rings. Electronic preprint arXiv:2308.16090 [math.RA], 41 pp. http://iitp.ru/https://arxiv.org/abs/2308.16090

Positselski L., Comodules and contramodules over coalgebras associated with locally finite categories. Electronic preprint arXiv:2307.13358 [math.CT], 35 pp. http://iitp.ru/https://arxiv.org/abs/2307.13358

Positselski L., Flat comodules and contramodules as directed colimits, and cotorsion periodicity. Electronic preprint arXiv:2306.02734 [math.RA], 44 pp. http://iitp.ru/https://arxiv.org/abs/2306.02734

Positselski L., Homological full-and-faithfulness of comodule inclusion and contramodule forgetful functors. Electronic preprint arXiv:2301.09561 [math.RA], 43 pp. http://iitp.ru/https://arxiv.org/abs/2301.09561

Positselski L., Šťovíček J., Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity. Electronic preprint arXiv:2212.09639 [math.AG], 28 pp. http://iitp.ru/https://arxiv.org/abs/2212.09639

Bazzoni S., Hrbek M., Positselski L., Fp-projective periodicity. Journ. of Pure and Appl. Algebra 228 #3 (2024), 107497, 24 pp. http://iitp.ru/https://arxiv.org/abs/2212.02300

Positselski L., Differential graded Koszul duality: An introductory survey. Bulletin of the London Math. Society 55 (2023), #4, p.1551-1640. http://iitp.ru/https://arxiv.org/abs/2207.07063

Positselski L., Semi-infinite algebraic geometry of quasi-coherent sheaves on ind-schemes: Quasi-coherent torsion sheaves, the semiderived category, and the semitensor product. Birkhäuser/Springer Nature, Cham, Switzerland, 2023. xix+216 стр. http://iitp.ru/https://arxiv.org/abs/2104.05517

Positselski L., Exact categories of topological vector spaces with linear topology. Electronic preprint arXiv:2012.15431 [math.CT], 71 pp. Accepted by Moscow Math. Journal. http://iitp.ru/https://arxiv.org/abs/2012.15431

Positselski L., Flat commutative ring epimorphisms of almost Krull dimension zero. Journ. of Algebra and its Appl. 22 #3 (2023), 2350060, 18 pp. http://iitp.ru/https://arxiv.org/abs/2009.03389

Positselski L., An explicit self-dual construction of complete cotorsion pairs in the relative context. Rendiconti Seminario Matematico Univ. Padova 149 (2023), p.191-253. http://iitp.ru/https://arxiv.org/abs/2006.01778

Positselski L., Remarks on derived complete modules and complexes. Mathematische Nachrichten 296 (2023), #2, p.811-839. http://iitp.ru/https://arxiv.org/abs/2002.12331

2022

Positselski L., Coderived and contraderived categories of locally presentable abelian DG-categories. Electronic preprint arXiv:2210.08237 [math.CT], 68 pp. http://iitp.ru/https://arxiv.org/abs/2210.08237

Positselski L., Příhoda P., Trlifaj J., Closure properties of \varinjlim \mathcal C. Journ. of Algebra 606 (2022), p.30-103. http://iitp.ru/https://arxiv.org/abs/2110.13105

Positselski L., Exact DG-categories and fully faithful triangulated inclusion functors. Electronic preprint arXiv:2110.08237 [math.CT], 151 pp. http://iitp.ru/https://arxiv.org/abs/2110.08237

Bazzoni S., Positselski L., Šťovíček J., Projective covers of flat contramodules. Internat. Math. Research Notices 2022, #24, p.19527-19564. http://iitp.ru/https://arxiv.org/abs/1911.11720

Positselski L., Relative nonhomogeneous Koszul duality. Frontiers in Mathematics, Birkhäuser/Springer Nature, Cham, Switzerland, 2021. xxix+278 pp. http://iitp.ru/https://arxiv.org/abs/1911.07402

Positselski L., Šťovíček J., Topologically semisimple and topologically perfect topological rings. Publicacions Matemàtiques 66 (2022), #2, p.457-540. http://iitp.ru/https://arxiv.org/abs/1909.12203

Positselski L., Pseudo-dualizing complexes of bicomodules and pairs of t-structures. Appl. Categor. Struct. 30 (2022), #2, p.379-416. http://iitp.ru/https://arxiv.org/abs/1907.03364

Hrbek M., Positselski L., Slávik A., Countably generated flat modules are quite flat. Journ. of Commutative Algebra 14 (2022), #1, p.37-54. http://iitp.ru/https://arxiv.org/abs/1907.00356

Positselski L., Contramodules over pro-perfect topological rings. Forum Mathematicum 34 (2022), #1, p.1-39. http://iitp.ru/https://arxiv.org/abs/1807.10671

Positselski L., Contramodules. Confluentes Math. 13 (2021), #2, p.93-182. http://arxiv.org/abs/1503.00991

2021

Positselski L., Šťovíček J., Derived, coderived, and contraderived categories of locally presentable abelian categories. Journ. of Pure and Appl. Algebra 226 #4 (2022), 106883, 39 pp. http://iitp.ru/https://arxiv.org/abs/2101.10797

Positselski L., Schnürer O., Unbounded derived categories of small and big modules: Is the natural functor fully faithful? Journ. of Pure and Appl. Algebra 225 #11 (2021), 106722, 23 pp. http://iitp.ru/https://arxiv.org/abs/2003.11261

Bazzoni S., Positselski L., Covers and direct limits: a contramodule-based approach. Math. Zeitschrift 299 (2021), #1-2, p.1-52. http://iitp.ru/https://arxiv.org/abs/1907.05537

Positselski L., Šťovíček J., The tilting-cotilting correspondence. Internat. Math. Research Notices 2021, #1, p.189-274. http://iitp.ru/https://arxiv.org/abs/1710.02230

2020

Lieberman M., Positselski L., Rosický J., Vasey S., Cofibrant generation of pure monomorphisms. Journal of Algebra 560 (2020), p.1297-1310. http://iitp.ru/https://arxiv.org/abs/2001.02062

Bazzoni S., Positselski L., Matlis category equivalences for a ring epimorphism. Journ. of Pure and Appl. Algebra 224 #10 (2020), 106398, 25 pp. http://iitp.ru/https://arxiv.org/abs/1907.04973

Positselski L., Flat ring epimorphisms of countable type. Glasgow Math. Journ. 62 (2020), #2, p.383-439. http://iitp.ru/https://arxiv.org/abs/1808.00937

Positselski L., Slávik A., Flat morphisms of finite presentation are very flat. Annali di Matematica Pura ed Applicata 199 (2020), #3, p.875-924. http://iitp.ru/https://arxiv.org/abs/1708.00846

Positselski L., Pseudo-dualizing complexes and pseudo-derived categories. Rendiconti Seminario Matematico Univ. Padova 143 (2020), p.153-225. http://iitp.ru/https://arxiv.org/abs/1703.04266

Positselski L., Smooth duality and co-contra correspondence. Journ. of Lie Theory 30 (2020), #1, p.85-144. http://arxiv.org/abs/1609.04597

2019

Adámek J., Brooke-Taylor A., Campion T., Positselski L., Rosický J., Colimit-dense subcategories. Commentationes Mathematicae Universitatis Carolinae 60 (2019), #4, p.447-462. http://iitp.ru/https://arxiv.org/abs/1812.10649

Positselski L., Šťovíček J., Exactness of direct limits for abelian categories with an injective cogenerator. Journ. of Pure and Appl. Algebra 223 (2019), #8, p.3330-3340. http://iitp.ru/https://arxiv.org/abs/1805.05156

Bazzoni S., Positselski L., S-almost perfect commutative rings. Journ. of Algebra 532 (2019), p.323-356. http://iitp.ru/https://arxiv.org/abs/1801.04820

Positselski L., Šťovíček J., Infinity-tilting theory. Pacific Journ. of Math. 301 (2019), #1, p.297-334. http://iitp.ru/https://arxiv.org/abs/1711.06169

Positselski L., Slávik A., On strongly flat and weakly cotorsion modules. Math. Zeitschrift 291 (2019), #3-4, p.831-875. http://iitp.ru/https://arxiv.org/abs/1708.06833

Positselski L., Weakly curved A-infinity algebras over a topological local ring. Mémoires de la Société Mathématique de France 159 (2018), vi+206 pp. http://arxiv.org/abs/1202.2697

2018

Positselski L., Rosický J., Nearly locally presentable categories. Theory and Appl. of Categories 33 (2018), #10, p.253-264. http://iitp.ru/https://arxiv.org/abs/1710.10476

Positselski L., Abelian right perpendicular subcategories in module categories. Electronic preprint arXiv:1705.04960 [math.CT], 57 pp. http://iitp.ru/https://arxiv.org/abs/1705.04960

Positselski L., Dedualizing complexes of bicomodules and MGM duality over coalgebras. Algebras and Represent. Theory 21 (2018), #4, p.737-767. http://arxiv.org/abs/1607.03066

Positselski L., Triangulated Matlis equivalence. Journ. of Algebra and its Appl. 17 #4 (2018), 1850067, 44 pp. http://arxiv.org/abs/1605.08018

Positselski L., Categorical Bockstein sequences. Appl. Categor. Struct. 26 (2018), #6, p.1211-1263. http://arxiv.org/abs/1404.5011

2017

Positselski L., Contraadjusted modules, contramodules, and reduced cotorsion modules. Moscow Math. Journal 17 (2017), #3, p.385-455. http://arxiv.org/abs/1605.03934

Positselski L., Rosický J., Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories. Journ. of Algebra 483 (2017), p.83-128. http://arxiv.org/abs/1512.08119

Positselski L., Koszulity of cohomology = K(pi,1)-ness + quasi-formality. Journ. of Algebra 483 (2017), p.188-229. http://arxiv.org/abs/1507.04691

Positselski L., Coherent rings, fp-injective modules, dualizing complexes, and covariant Serre-Grothendieck duality. Selecta Math. New Ser. 23 (2017), #2, p.1279-1307. http://arxiv.org/abs/1504.00700

Positselski L., Contraherent cosheaves. Electronic preprint arXiv:1209.2995 [math.CT], 257 pp. http://arxiv.org/abs/1209.2995

2016

Positselski L., Noncommutative Kummer theory. Electronic preprint arXiv:1606.03880 [math.KT], 7 pp. http://arxiv.org/abs/1606.03880

Positselski L., Dedualizing complexes and MGM duality. Journ. of Pure and Appl. Algebra 220 (2016), #12, p.3866-3909. http://arxiv.org/abs/1503.05523

2015

Efimov A.I., Positselski L., Coherent analogues of matrix factorizations and relative singularity categories. Algebra and Number Theory 9 (2015), #5, p.1159-1292. http://arxiv.org/abs/1102.0261

Positselski L., Artin-Tate motivic sheaves with finite coefficients over an algebraic variety. Proceedings of the London Math. Soc. 111 (2015), #6, p.1402-1430. http://arxiv.org/abs/1012.3735

2014

Positselski L., Galois cohomology of a number field is Koszul. Journ. of Number Theory 145 (2014), p.126-152. http://arxiv.org/abs/1008.0095

2012

Polishchuk A., Positselski L., Hochschild (co)homology of the second kind I. Transactions of the Amer. Math. Soc. 364 (2012), #10, p.5311-5368. http://arxiv.org/abs/1010.0982

Positselski L., The algebra of closed forms in a disk is Koszul. Funct. Anal. Appl. 46 (2012), #3, p.218-224. http://arxiv.org/abs/1007.5010

2011

Positselski L., Mixed Artin-Tate motives with finite coefficients. Moscow Math. Journal 11 (2011), #2, p.317-402. http://arxiv.org/abs/1006.4343

Positselski L., Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence. Memoirs of the Amer. Math. Soc. 212 (2011), #996, vi+133 pp. http://arxiv.org/abs/0905.2621

2010

Positselski L., Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures. Appendix C in collaboration with D.Rumynin; Appendix D in collaboration with S.Arkhipov. Monografie Matematyczne, vol.70, Birkhäuser/Springer Basel, 2010. xxiv+349 pp. http://arxiv.org/abs/0708.3398

Bezrukavnikov R., Positselski L., On semi-infinite cohomology of finite-dimensional graded algebras. Compositio Math. 146 (2010), #2, p.480-496. http://arxiv.org/abs/0803.3252

2006

Positselski L., Galois cohomology of certain field extensions and the divisible case of Milnor-Kato conjecture. K-Theory 36 (2005), #1-2, p.33-50. http://arxiv.org/abs/math/0209037

2005

Positselski L., Koszul property and Bogomolov`s conjecture. Internat. Math. Research Notices 2005, #31, p.1901-1936. http://arxiv.org/abs/1405.0965

Polishchuk A., Positselski L., Quadratic Algebras. University Lecture Series 37. American Mathematical Society, Providence, RI, 2005. xii+159 pp. http://www.ams.org/bookstore?fn=20&arg1=ulectseries&ikey=ULECT-37

2002

Bezrukavnikov R., Braverman A., Positselski L., Gluing of abelian categories and differential operators on the basic affine space. Journ. Inst. Math. Jussieu 1 (2002), #4, p. 543-557. http://arxiv.org/abs/math/0104114

1999

Positselski L., Mixed Tate motives with finite coefficients and conjectures about the Galois groups of fields. Abstracts of conference talks, "Algebraische K-theorie", Tagungsbericht 39/1999, September-October 1999, Oberwolfach, Germany, p.8-9. http://www.mfo.de/document/9939/Report_39_99.ps

1995

Positselski L., Relation between the Hilbert series of quadratic dual algebras does not imply Koszulity. Funct. Anal. Appl. 29 (1995) #3, p.213-217. http://mi.mathnet.ru/faa604

Positselski L., All strictly exceptional collections in D^b_{coh}(P^m) consist of vector bundles. Electronic preprint arXiv:alg-geom/9507014, 6 pp. http://arxiv.org/abs/alg-geom/9507014

Positselski L., Vishik A., Koszul duality and Galois cohomology. Math. Research Letters 2 (1995), #6, p.771-781. http://arxiv.org/abs/alg-geom/9507010

1993

Positselski L., Nonhomogeneous quadratic duality and curvature. Funct. Anal. Appl. 27 (1993) #3, p.197-204. http://mi.mathnet.ru/faa712

1991

Positselski L., Local Pluecker formulas for a semisimple Lie group. Funct. Anal. Appl. 25 (1991) #4, p. 291-292. http://mi.mathnet.ru/faa902