Related papers: Shokurov's index conjecture for quotient singulari…
We prove that finite index subgroups in S-arithmetic Chevalley groups are bounded.
We give a short proof and some strengthening of the Khukhro--Makarenko theorem that each group virtually satisfying an outer commutator identity contains a finite-index characteristic subgroup satisfying this identity. An estimate for the…
We present an elementary proof for Ljunggren equation
In this paper, we prove the Effective Bogomolov's Conjecture for hyperelliptic curves defined over function fields.
We show that finite index quantum subgroups of a discrete quantum group are induced from finite index quantum subgroups of the unimodularization. As an application, we classify all finite index quantum subgroups of free products of the…
The present article gives the index formula of the principal congruence subgroups of the Hecke group H_5
In this article we formulate a version of the analytic Novikov conjecture for semigroups rather than groups, and show that the descent argument from coarse geometry generalises effectively to this new situation.
We use the geometric reformulation of Markov's uniqueness conjecture in terms of the simple length spectrum on the modular torus to rewrite the conjecture in combinatorial terms by explicitly describing this set of lengths.
We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
We prove a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms. Our results are inspired by and analogous to recent results for diagonal quadratic forms due to Bourgain.
We present a general conjecture on the divisibility of a certain expression in terms of Kostka numbers and their close variants. This conjecture is closely related to a variant of the period-index problem of noncommutative algebra, with…
We prove Burkholder inequality using Bregman divergence.
We present an alternative approach to the vector version of Krasnosel'skii compression-expansion fixed point theorem due to Precup, which is based on the fixed point index. It allows us to obtain new general versions of this fixed point…
We introduce a version of the Alexander polynomial for singular knots and tangles and show how it can be strengthened considerably by introducing a perturbation. For singular long knots, we also prove that our Alexander polynomial agrees…
We prove the Jacobian Conjecture for the space of all the inner functions in the unit disc.
In this note we verify the equivalent version of Huppert's conjecture for $K_3$-groups.
Here we outline a proof for the 4-dimensional smooth Poincare Conjecture.
We prove Fujita's freeness conjecture for Gorenstein complexity-one $T$-varieties with rational singularities.
We study the conjecture due to V.\,V. Shokurov on characterization of toric varieties. We also consider one generalization of this conjecture. It is shown that none of the characterizations holds true in dimension $\ge 3$. Some weaker…