Related papers: A glimpse into Rokhlin's Signature Divisibility Th…
It was proved in [3] that every h-divisible modules admits an strongly flat cover over all integral domains; and every divisible module over an integral domain R admits a strongly flat cover if and only if R is a Matlis domain. In this…
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
It is known that there are infinitely-many prime numbers which take the form of a polynomial of degree one with integer coefficients, this is Dirichlet's theorem. We use an elementary sieving argument together with bounds on the prime…
We study a family of identities regarding a divisibility property of the Kostant partition function which first appeared in a paper of Baldoni and Vergne. To prove the identities, Baldoni and Vergne used techniques of residues and called…
Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
The notice provides some critical remarks on a paper (preprint) by V.A.Sharafutdinov. The remarks mainly concern Theorem 1.1 on determination of the Riemann surface from its Dirichlet-to-Neuman map, which is declared as one of the basic…
We generalize Iskovskih's theorem about surfaces without irregularity and bigenus from the smooth case to regular surfaces over arbitrary fields, with special focus on the case of imperfect fields. This includes surfaces that are…
We give a "soft" proof of Alberti's Luzin-type theorem in [1] (G. Alberti, A Lusintype theorem for gradients, J. Funct. Anal. 100 (1991)), using elementary geometric measure theory and topology. Applications to the $C^2$-rectifiability…
This work consists of two parts. In the first part, we consider a compact connected strongly pseudoconvex CR manifold $X$ with a transversal CR $S^{1}$ action. We establish an equidistribution theorem on zeros of CR functions. The main…
The Petrov classification is an important algebraic classification for the Weyl tensor valid in 4-dimensional space-times. In this thesis such classification is generalized to manifolds of arbitrary dimension and signature. This is…
We provide an asymptotic expression for the probability that a randomly chosen polynomial with given degree, having integral coefficients bounded by some B, has a prescribed signature. We also give certain related formulas and numerical…
Recent work alludes to various `controversies' associated with signature change in general relativity. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible…
We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
We prove that a contractible orbifold is a manifold.
The paper is devoted to a generalized and improved version of author's approach to Gromov bounded cohomology theory. In particular, the awkward countability assumption is removed and the aspects related to homological algebra are clarified.…
This expository paper contains a detailed introduction to some important works concerning the Gauss-Bonnet-Chern theorem. The study of this theorem has a long history dating back to Gauss's Theorema Egregium (Latin: Remarkable Theorem) and…
We prove a version of the Manin-Mumford conjecture for semiabelian varieties over fields of positive characteristic. The proof presented here contains the details of the proof sketched by the author in the article "Diophantine geometry from…
This work represents a translation from English into Russian of the first part of the monograph by Alexander Kiselev under the same title, containing the proof (in ZF) of inaccessible cardinals nonexistence. The first edition of this work…