Related papers: The Heyde Theorem on a-adic Solenoids

We construct an analog of the Hodge theory on complex manifolds on tropical curves. We use the analytical approach to the problem, it is based on language of tropical differential forms and methods of $L^2-$cohomologies.

We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.

We motivate and then prove a generalized pythagorean theorem for parallelepipeds in Euclidean space.

New version, including a variant of Quillen's proof of the Solomon-Tits theorem.

The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

We prove the analogue of Helly's theorem for systolic complexes. Namely, we show that 7-systolic complexes have Helly dimension less or equal to 1, whereas 6-systolic complexes have Helly dimension bounded from the above by 2.

We prove an analogue of the fixed-point theorem for the case of definably amenable groups.

We give a new simpler proof of a theorem of Jayne and Rogers.

In this article, we prove a decomposition theorem on differential polynomials of theta functions of high level.

This note presents a new equivalence to the Riemann Hypothesis by means of the Salem integral equation.

An analogue of the Gauss-Lucas theorem for polynomials over the algebraic closure $\mathbb C_p$ of the field of $p$-adic numbers is considered.

The analog of the Schauder inequality for closed surfaces in Euclidean spaces is obtained in this article.

A proof of Sendov's conjecture is given.

We generalize the Ahlfors-Bers theory to the adelic Riemann sphere. In particular, after defining the appropriate notion of a Beltrami differential in the solenoidal context, we give a sufficient condition on it such that the corresponding…

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

We formulate and prove an analogue of Beurling's theorem for the Fourier transform on the Heisenberg group. As a consequence we deduce Hardy and Cowling-Price theorems.

We prove an analog of Gromov--Lawson type relative index theorems for K-homology classes.

We prove Haynes' version of the Duffin--Schaeffer conjecture for the $p$-adic numbers. In addition, we prove several results about an associated related but false conjecture, related to $p$-adic approximation in the spirit of Jarn\'ik and…

An equivalent but useful version on the Homological Nerve Theorem is proved.

Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie…