Algebraic and arithmetic geometry,
algebraic number theory,
higher adeles and higherdimensional local fields,
2-categories and their applications to higher adeles and arithmetic, higherdimensional reciprocity laws, discrete Heisenberg groups, local Riemann-Roch theorems,
integrable systems.
Main publications:
D. V. Osipov, A. N. Parshin, “Harmonic analysis on the rank-$2$ value group of a two-dimensional local field”, Sb. Math., 211:1 (2020), 115–160 , arXiv: 1911.09718
Denis Osipov, Xinwen Zhu, “The two-dimensional Contou-Carrère symbol and reciprocity laws”, J. Algebraic Geom., 25 (2016), 703–774 , arXiv: 1305.6032
D. V. Osipov, “The unramified two-dimensional Langlands correspondence”, Izv. Math., 77:4 (2013), 714–741 , arXiv: 1210.3780
Denis Osipov, Xinwen Zhu, “A categorical proof of the Parshin reciprocity laws on algebraic surfaces”, Algebra Number Theory, 5:3 (2011), 289–337 , arXiv: 1002.4848
D. Osipov, “Adeles on $n$-dimensional schemes and categories $C_n$”, Internat. J. Math., 18:3 (2007), 269–279 , arXiv: math/0509189
D. V. Osipov, “Krichever correspondence for algebraic varieties”, Izv. Math., 65:5 (2001), 941–975 , arXiv: math/0003188
D. V. Osipov, “Adele constructions of direct images of differentials and symbols”, Sb. Math., 188:5 (1997), 697–723 , arXiv: math/9802112
D. V. Osipov, “Formal Bott–Thurston Cocycle and Part of a Formal Riemann–Roch Theorem”, Proc. Steklov Inst. Math., 320 (2023), 226–257 , arXiv: 2211.15932
3.
D. V. Osipov, “Determinant central extension and $\cup$-products of 1-cocycles”, Russian Math. Surveys, 78:4 (2023), 791–793
4.
D. V. Osipov, “Central extensions and the Riemann-Roch theorem on algebraic surfaces”, Sb. Math., 213:5 (2022), 671–693 , arXiv: 2105.14626
5.
D. V. Osipov, “Vospominaniya ob A. N. Parshine”, Vospominaniya ob A. N. Parshine, ISBN 978-5-4439-1767-2, MTsNMO, Moskva, 2022, 16-18tekst zametki
6.
D. V. Osipov, A. N. Parshin, “Harmonic analysis on the rank-$2$ value group of a two-dimensional local field”, Sb. Math., 211:1 (2020), 115–160 , arXiv: 1911.09718
7.
S. O. Gorchinskiy, D. V. Osipov, “The higher-dimensional Contou-Carrère symbol and commutative group schemes”, Russian Math. Surveys, 75:3 (2020), 572–574
8.
S. O. Gorchinskiy, D. V. Osipov, “Iterated Laurent series over rings and the Contou-Carrère symbol”, Russian Math. Surveys, 75:6 (2020), 995–1066
9.
A. B. Zheglov, D. V. Osipov, “Lax pairs for linear Hamiltonian systems”, Siberian Mathematical Journal, 60:4 (2019), 592–604https://rdcu.be/bON6F, arXiv: 1901.11130
10.
D. V. Osipov, “Grothendieck–Serre duality and theta-invariants on arithmetic surfaces”, Doklady Mathematics, 100:1 (2019), 385–388
11.
D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Mathematical Journal, 30 (2019), 111–122 , arXiv: 1706.09826
12.
D. V. Osipov, “Arithmetic surfaces and adelic quotient groups”, Izv. Math., 82:4 (2018), 817–836 , arXiv: 1801.02282
13.
A. B. Zheglov, D. V. Osipov, “On first integrals of linear Hamiltonian systems”, Dokl. Math., 98:3 (2018), 616–618
14.
Denis V. Osipov, “Second Chern numbers of vector bundles and higher adeles”, Bull. Korean Math. Soc., 54:5 (2017), 1699–1718 , arXiv: 1706.07354
15.
Denis Osipov, Xinwen Zhu, “The two-dimensional Contou-Carrère symbol and reciprocity laws”, J. Algebraic Geom., 25 (2016), 703–774 , arXiv: 1305.6032
D. V. Osipov, A. N. Parshin, “Representations of the Discrete Heisenberg Group on Distribution Spaces of Two-Dimensional Local Fields”, Proc. Steklov Inst. Math., 292 (2016), 185–201 , arXiv: 1510.02423
17.
Sergey O. Gorchinskiy, Denis V. Osipov, “Continuous homomorphisms between algebras of iterated Laurent series over a ring”, Proc. Steklov Inst. Math., 294 (2016), 47–66
18.
S. O. Gorchinskiy, D. V. Osipov, “Higher-dimensional Contou-Carrère symbol and continuous automorphisms”, Funct. Anal. Appl., 50:4 (2016), 268–280
19.
S. O. Gorchinskiy, D. V. Osipov, “Explicit formula for the higher-dimensional Contou-Carrère symbol”, Russian Math. Surveys, 70:1 (2015), 171–173
20.
S. O. Gorchinskiy, D. V. Osipov, “A higher-dimensional Contou-Carrère symbol: local theory”, Sb. Math., 206:9 (2015), 1191–1259 , arXiv: 1505.03829
21.
D. V. Osipov, “The Discrete Heisenberg Group and Its Automorphism Group”, Math. Notes, 98:1 (2015), 185–188 , arXiv: 1505.00348
22.
S. O. Gorchinskiy, D. V. Osipov, “Tangent Space to Milnor $K$-Groups of Rings”, Proc. Steklov Inst. Math., 290 (2015), 26–34 , arXiv: 1505.03780
23.
H. Kurke, D. Osipov, A. Zheglov, “Commuting differential operators and higher-dimensional algebraic varieties”, Selecta Math. (N.S.), 20:4 (2014), 1159–1195 , arXiv: 1211.0976
D. V. Osipov, “The unramified two-dimensional Langlands correspondence”, Izv. Math., 77:4 (2013), 714–741 , arXiv: 1210.3780
25.
D. V. Osipov, “Noncommutative reciprocity laws on algebraic surfaces: the case of tame ramification”, Sb. Math., 204:12 (2013), 1797–1810 , arXiv: 1307.1995
26.
D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II”, Izv. Math., 75:4 (2011), 749–814 , arXiv: 0912.1577
27.
Denis Osipov, Xinwen Zhu, “A categorical proof of the Parshin reciprocity laws on algebraic surfaces”, Algebra Number Theory, 5:3 (2011), 289–337 , arXiv: 1002.4848
D. V. Osipov, A. N. Parshin, “Harmonic analisys and the Riemann-Roch theorem”, Dokl. Math., 84:3 (2011), 826–829 , arXiv: 1107.0408
29.
Herbert Kurke, Denis V. Osipov, Alexander B. Zheglov, “Formal groups arising from formal punctured ribbons”, Inernat. J. Math., 21:6 (2010), 755–797 , arXiv: 0901.1607
H. Kurke, D. Osipov, A. Zheglov, “Formal punctured ribbons and two-dimensional local fields”, J. Reine Angew. Math., 629 (2009), 133–170 , arXiv: 0708.0985
A. B. Zheglov, D. V. Osipov, “Higher KP-hierarchies and punctured ribbons”, Modern problems of mathematics and mechanics. Volume III “Mathematics”, Issue 2 “Geometry and topology”, eds. A. T. Fomenko, Moscow State University, Moscow, 2009, 15–35 (in Russian)
32.
D. V. Osipov, “$n$-dimensional local fields and adeles on $n$-dimensional schemes”, Surveys in Contemporary Mathematics, London Mathematical Society Lecture Note Series, 347, Cambridge University Press, Cambridge, 2008, 131–164 arXiv: math/0508205
A. B. Zheglov, D. V. Osipov, “On Some Questions Related to the Krichever Correspondence”, Math. Notes, 81:4 (2007), 467–476 , arXiv: math/0610364
36.
D. V. Osipov, “Central extensions and reciprocity laws on algebraic surfaces”, Sb. Math., 196:10 (2005), 1503–1527 , arXiv: math/0501155
37.
D. V. Osipov, “The infinite-dimensional Sato Grassmannian and coherent sheaves of rank 2 on curves”, Sb. Math., 194:11 (2003), 1665–1678 , arXiv: math/9904152
38.
D. V. Osipov, “Krichever correspondence for algebraic varieties”, Izv. Math., 65:5 (2001), 941–975 , arXiv: math/0003188
39.
Osipov Denis, “Adelic constructions for direct images of differentials and symbols”, Invitation to higher local fields (Münster, 1999), Geom. Topol. Monogr., 3, Geom. Topol. Publ., Coventry, 2000, 215–221 arXiv: math/0012152 (electronic)
40.
D. V. Osipov, “The Krichever map and (semi)stable sheaves on curves”, Russian Math. Surveys, 54:3 (1999), 646–647
41.
D. V. Osipov, “Adele constructions of direct images of differentials and symbols”, Sb. Math., 188:5 (1997), 697–723 , arXiv: math/9802112
Thesis
42.
D. V. Osipov, Kategornye metody v teorii vysshikh adelei i ikh primenenie, Diss. … dokt. fiz.-matem. nauk, Matematicheskii institut im. V. A. Steklova RAN, Moskva, 2013 , 195 pp. avtoreferat dissertatsii
Proceedings
43.
D. V. Osipov, “Dvumernoe sootvetstvie Lenglendsa”, Algebra i teoriya chisel: sovremennye problemy i prilozheniya: Tezisy dokladov XI Mezhdunarodnoi konferentsii (Saratov, 9–14 sentyabrya 2013 g.), ISBN 978-5-292-04189-4, Izdatelstvo Saratovskogo universiteta, Saratov, 2013, 64–65old.sgu.ru/files/nodes2013/67438/Tezis.pdf
44.
D. V. Osipov, “Vvedenie v teoriyu vysshikh adelei”, programma lektsii, Letnyaya shkola-konferentsiya po algebraicheskoi geometrii i kompleksnomu analizu dlya molodykh uchenykh Rossii (Yaroslavl, YaGPU, 20–25 maya 2013 g.), Matematicheskii institut im. V. A. Steklova RAN, Moskva, 2013, 8–9
ArXiv
45.
Denis Osipov, To the multidimensional tame symbol, 2003 , 27 pp., preprint 03-13 of the Humboldt University of Berlin, arXiv: 1105.1362
Personalia
46.
F. A. Bogomolov, A. M. Vershik, S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarhin, S. V. Konyagin, Vik. S. Kulikov, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, I. A. Panin, V. P. Platonov, V. L. Popov, Yu. G. Prokhorov, A. L. Smirnov, “Alexey Nikolaevich Parshin (obituary)”, Russian Math. Surveys, 78:3 (2023), 549–554
47.
S. O. Gorchinskiy, Vik. S. Kulikov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, V. L. Popov, N. A. Tyurin, G. B. Shabat, A. I. Shafarevich, V. V. Shokurov, “Igor Rostislavovich Shafarevich (on the centenary of his birthday)”, Russian Math. Surveys, 78:6 (2023), 1167–1178
48.
F. A. Bogomolov, S. O. Gorchinskiy, A. B. Zheglov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, A. N. Parshin, V. L. Popov, V. V. Przyjalkowski, Yu. G. Prokhorov, M. Reid, A. G. Sergeev, D. V. Treschev, A. K. Tsikh, I. A. Cheltsov, E. M. Chirka, “Viktor Stepanovich Kulikov (on his 70th birthday)”, Russian Math. Surveys, 77:3 (2022), 555–557
49.
S. O. Gorchinskiy, N. M. Dobrovol'skii, A. B. Zheglov, D. V. Osipov, “In memory of Alexey Nikolaevich Parshin”, Chebyshevskii Sb., 23:3 (2022), 306–307
50.
S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197
Miscellaneous
51.
Algebra, arifmeticheskaya, algebraicheskaya i kompleksnaya geometriya, Sbornik statei. Posvyaschaetsya pamyati akademika Alekseya Nikolaevicha Parshina, Trudy MIAN, 320, ed. V. L. Popov, S. O. Gorchinskii, A. B. Zheglov, D. V. Osipov, MIAN, M., 2023 , 324 pp.
Отдел алгебры S. O. Gorchinskiy, D. V. Osipov Conference MIAN-90, dedicated to the 90th anniversary of Steklov Mathematical Institute May 13, 2024 16:30
Формальный коцикл Ботта и детерминантное центральное расширение D. V. Osipov XXI International Conference «Algebra, Number Theory, Discrete Geometry and Multiscale Modeling: Modern Problems, Applications and Problems of History», Dedicated to the 85th Anniversaryof the Birth of A. A. Karatsuba May 18, 2022 12:10
Higher-dimensional Contou-Carrere symbols D. V. Osipov Conference «Contemporary Mathematics and its applications» dedicated to the results of research supported by the Russian Science Foundation grant 14-50-00005 November 19, 2018 14:40
Многомерное соответствие Кричевера–Паршина D. V. Osipov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) October 11, 2006
Algebra and Arithmetic, Algebraic, and Complex Geometry, Collected papers. In memory of Academician Alexey Nikolaevich Parshin, Trudy Mat. Inst. Steklova, 320, ed. V. L. Popov, S. O. Gorchinskiy, A. B. Zheglov, D. V. Osipov, 2023, 324 с. http://mi.mathnet.ru/book1934