Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: Keywords: algebraic variety,
arithmetic surface,
higherdimensional local field,
higher adeles,
2-category,
reciprocity law,
harmonic analysis.
Subject:
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
