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Strong Suslin Reciprocity Law and the Norm map
Mathematical notes. 2022. Vol. 1. No. 112. P. 309–312.
In press
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
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
Rudenko D., Functional Analysis and Its Applications 2016 Vol. 50 No. 1 P. 66–70
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 ...
Added: May 4, 2016
Cherednik I., Feigin B. L., Advances in Mathematics 2013 Vol. 248 No. 25 P. 1050–1088
Using the DAHA-Fourier transform of q-Hermite polynomials multiplied by level-one theta functions, we obtain expansions of products of any number of such theta functions in terms of the q-Hermite polynomials. An ample family of modular functions satisfying Rogers-Ramanujan type identities for arbitrary (reduced, twisted) affine root systems is obtained as an application. A relation to ...
Added: September 30, 2013