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The Strong Suslin Reciprocity Law and Its Applications to Scissor Congruence Theory in Hyperbolic Space
Functional Analysis and Its Applications. 2016. Vol. 50. No. 1. P. 66–70.
Rudenko D.
We prove the strong Suslin reciprocity law conjectured by A. B. Goncharov and describe its corollaries for the theory of scissor congruence of polyhedra in hyperbolic space. The proof is based on the study of Goncharov’s conjectural description of certain rational motivic cohomology groups of a field. Our main result is a homotopy invariance theorem for these groups.
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Панин И. А., Tyurin D., Алгебра и анализ 2025 Т. 37 № 6 С. 148–157
Пусть $F$ является $\mathbb{A}^{1}$-инвариантным квази-стабильным $\mathbb{Z}F_{\ast}$-предпучком. Тогда соответствующий пучок Зарисского $F_{Zar}$ совпадает с пучком Нисневича $F_{Nis}$. Кроме того, для любой $k$-гладкой схемы $X\in Sm/k$ имеют место равенства $H^{n}_{Zar}(X, F_{Zar})=H^{n}_{Nis}(X,F_{Nis})$. ...
Added: September 24, 2025
Bayramov Ilyas, / Series math "arxiv.org". 2024.
Added: September 16, 2024
Bolbachan V., Journal of Algebraic Geometry 2023 Vol. 32 No. 4 P. 697–728
We prove a conjecture of A. Goncharov concerning strong Suslin reciprocity law. The main idea of the proof is the construction of the norm map on so-called lifted reciprocity maps. This construction is similar to the construction of the norm map on Milnor K-theory. As an application, we express Chow dilogarithm in terms of Bloch-Wigner ...
Added: September 28, 2023
Bolbachan V., / Series math.AG "arXiv:2108.11862 [math.AG]". 2021.
We prove a conjecture of A. Goncharov about so-called strong reciprocity laws. The main idea of the proof is the construction of the norm map on these strong reciprocity laws. This construction is very similar to the construction of the norm map on Milnor K-theory. As an application, we prove a new relation for Bloch-Wigner dilogarithm ...
Added: August 29, 2021
Vostokov S. V., Афанасьева С. С., Bondarko M. V. et al., Vestnik St. Petersburg University: Mathematics 2017 Vol. 50 No. 3 P. 242–264
—This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems ...
Added: April 19, 2021
Smirnov E., Квант 2019 № 10 С. 2–11
Статья посвящена изложению основных фактов о квадратичных вычетах. Мы приводим доказательство Эйзенштейна квадратичного закона взаимности Гаусса. ...
Added: July 6, 2020
Chetverikov V., Journal of Physics: Conference Series 2019 Vol. 1163 No. 012077 P. 1–6
A theoretical model describing the spontaneous magnetization of a ferromagnetic semiconductor (InMn)As film in the presence of an external electric field directed across the film is considered. It is assumed that the ions of a manganese impurity with spin 5/2 are acceptors, have a uniform spatial distribution inside the semiconductor, and do not change their ...
Added: April 2, 2019
Chetverikov V., Moscow University Physics Bulletin 2018 Vol. 73 No. 6 P. 592–598
A model for the description of the distribution of magnetization across the thickness of a ferromagnetic
semiconductor film is considered. Applying a constant electric field perpendicular to the film surface
makes it possible to change the Curie temperature. The obtained formulas determine the dependence
that this distribution has on the values of the physical parameters of the film. ...
Added: March 1, 2019
Chetverikov V., Вестник Московского университета. Серия 3: Физика и астрономия 2018 № 6 С. 28–33
A model for describing the distribution of magnetization over the thickness of a film of a ferromagnetic
semiconductor in an external constant electric field perpendicular to the film surface is considered. The
formulas obtained make it possible to determine the dependence of this distribution on the values of the
physical parameters of the film. ...
Added: March 1, 2019
Beilinson A., Kungs G., Levin A., Mathematische Annalen 2018 Vol. 371 No. 3-4 P. 1449–1495
We develop the topological polylogarithm which provides an integral version of Nori’s Eisenstein cohomology classes for GLn (Z) and yields classes with
values in an Iwasawa algebra. This implies directly the integrality properties of special values of L-functions of totally real fields and a construction of the associated
p-adic L-function. Using a result of Graf, we also ...
Added: January 26, 2018