Related papers: Finiteness Problems in Diophantine Geometry
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…
This is an English translation of Moufang's notes "Grundlagen der Geometrie" at the University of Frankfurt in 1948, with added notes by the translator.
In this note, we present an improvement to a recent result due to Beresnevich, Levesley, and Ward (2021) pertaining to weighted simultaneous Diophantine approximation on manifolds.
This paper contains first results on the finite-gap integration of the Sine-Gordon equation. They were published on Russian in 1976. The papers \cite{Koz}, \cite{KK}, \cite{KK02} have been rewritten in the English language with small…
This is an extended version of a talk on October 4, 2004 at the research seminar ``Differential geometry and applications'' (headed by Academician A. T. Fomenko) at Moscow State University. The paper contains an overview of available (but…
This note contains a correction of the proofs of the main results of the paper [A. Yekutieli, Deformation quantization in algebraic geometry, Adv. Math. 198 (2005), 383-432]. The results are correct as originally stated.
These notes grew out of an expose on M. Gromov's paper "Convex sets and K\"ahler manifolds'' ("Advances in Differential Geometry and Topology,'' World Scientific, 1990) at the DMV-Seminar on "Combinatorical Convex Geometry and Toric…
This note provides a brief guide to the current state of the literature on Tarski's problems with emphasis on features that distinguish the approach based on combinatorial and algorithmic group theory from the topological approach to…
This is an overview article on selected topics in symplectic geometry written for the Handbook of Differential Geometry (volume 2, edited by F.J.E. Dillen and L.C.A. Verstraelen).
This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of…
This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are…
Expanded version of the author's contribution to the Concise Encyclopaedia of Supersymmetry, eds. J. Bagger, S. Duplij and W. Siegel
In the recent paper arXiv:1807.02721, B. Lawrence and A. Venkatesh develop a method of proving finiteness theorems in arithmetic geometry by studying the geometry of families over a base variety. Their results include a new proof of both…
This paper re-organizes Vojta's proof of the Mordell conjecture (i.e. Faltings' theorem) in terms of Arakelov geometry. A new ingredient is to replace an application of Gillet--Soule's arithmetic Riemannn--Roch theorem by that of Yuan's…
This is an English translation of the thesis written by G. S. Makanin for the degree of Candidate of Physical and Mathematical Sciences (equivalent to a Ph.D.), originally submitted to the Steklov Mathematical Institute in 1966. The…
This is an essay to accompany the author's lecture at the introductory workshop on `Nonabelian fundamental groups in arithmetic geometry' at the Newton Institute, Cambridge in July, 2009.
This contains Part I of the book: Congruence lattices of finite lattices, which covers about 80 years of research and more than 250 papers.
This is the article with the same title which is scheduled to appear in the January 2022 issue of the AMS Notices, with additional references which could not be provided in the accepted version due to space constraints. The figures in this…
6 pages, LaTeX, to appear in Proc. of International Conf. "Geometrization of Physics - II", Kazan, Russia, Oct 28 - Nov 2, 1995. Withdrawn
We give an alternative proof of Faltings's theorem (Mordell's conjecture): a curve of genus at least two over a number field has finitely many rational points. Our argument utilizes the set-up of Faltings's original proof, but is in spirit…