Related papers: Remark on Faltings theorem
In this paper, we prove a version of the logarithmic Sobolev inequality of fractional order on noncommutative $n$-tori for any dimension $n\geq 2$.
We prove a model theoretic Baire category theorem for $\tilde\tau_{low}^f$-sets in a countable simple theory in which the extension property is first-order and show some of its applications. We also prove a trichotomy for minimal types in…
Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation finite algebra by Riedtmann and later for finite dimensional algebras by Bongartz and Gabriel, R. Martinez-Villa and de…
In this paper, we provide a fairly general self-reference-free proof of the Second Incompleteness Theorem from Tarski's Theorem of the Undefinability of Truth.
We prove Roth type theorems in finite groups. Our main tool is the Triangle Removal Lemma of Ruzsa and Szemer\'edi.
We establish a Liouville type theorem for some conformally invariant fully nonlinear equations
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
We state a simple criterion to prove the infiniteness of the image of Reshetikhin-Turaev irreducible representations of the mapping class groups of surfaces. We use it to study some of the Reshetikhin-Turaev representations associated to…
We demonstrate a construction of products on the quantum torus $\mathbb{T}_\theta^2$ that generalises the usual construction of finite Riesz products on the commutative torus $\mathbb{T}^2$. We explain why the former constitutes a natural…
We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.
An analogue of Gross' logarithmic Sobolev inequality for a class of elements of noncommutative two tori is proved.
We develop silting theory of a noetherian algebra $\Lambda$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $\Lambda$, and as a consequence, we see that mutation exists. As in the case of…
We defined a notion of quantum 2-torus $T_\theta$ in "Masanori Itai and Boris Zilber, Notes on a model theory of quantum 2-torus $T_q^2$ for generic $q$, arXiv:1503.06045v1 [mathLO]" and studied its model theoretic property. In this note we…
We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need…
In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.
The first effective versions of Faltings product theorem are given by J.H. Evertse and R. Ferretti. Their results are improved quantitatively by P. Philippon, thanks to Samuel's multiplicity instead of the length in his zeros estimate. This…
We offer a solution to a functional equation using properties of the Mellin transform. A new criteria for the Riemann Hypothesis is offered as an application of our main result, through a functional relationship with the Riemann xi…
Using a result of M. Hochster and C. Huneke on $F$-rational rings a criterion for complete intersection rings of characteristic $p>0$ is presented. As an application, we give a completely different proof for an algebraic result of G.…
We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem (alternatively, one can think of these proofs as using Hindman's theorem). This adds to the existing…
Using the ideas of Deninger, we prove that the Artin $L$-functions coincide with such of the noncommutative tori. This result can be viewed as the Langlands reciprocity for noncommutative tori.