Related papers: Strong approximation for certain quadric fibration…

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…

We study the failure of the integral Hasse principle and strong approximation for the Erd\H{o}s-Straus conjecture using the Brauer-Manin obstruction.

We show that badly approximable matrices are exactly those that, for any inhomogeneous parameter, can not be inhomogeneous approximated at every monotone divergent rate, which generalizes Ram\'irez's result (2018). We also establish some…

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…

We study local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, we develop a semi-integral version of the Brauer-Manin obstruction interpolating between Manin's classical…

By studying $\mathbb{A}^1$-curves on varieties, we propose a geometric approach to strong approximation problem over function fields of complex curves. We prove that strong approximation holds for smooth, low degree affine complete…

Let X be a homogeneous space, X = G/H, where G is a connected linear algebraic group over a number field k, and H is a k-subgroup of G (not necessarily connected). Let S be a finite set of places of k. We compute the Brauer-Manin…

We prove that the Brauer-Manin obstruction is the only obstruction to the Hasse principle and to the weak approximation for zero-cycles on certain fibrations over a smooth curve or over the projective space. The principal novelty is that…

The paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers, i.e., is homotopic to Manifold Approximate Fibration. We define obstructions in algebraic K-theory.…

Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate…

We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subspaces satisfying a highly generic and essentially optimal…

Approximation theorems for algebraic stacks over a number field $k$ are studied in this article. For G a connected linear algebraic group over a number field we prove strong approximation with Brauer-Manin obstruction for the classifying…

In this paper, we construct three kinds of Ch\^atelet surfaces, which have some given arithmetic properties with respect to field extensions of number fields. We then use these constructions to study the properties of weak approximation…

We prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt games. In particular, under certain restrictions we give a affirmative answer to the analogue in this setting of a famous conjecture of…

We study fibrations of the projective model for the symmetric space associated with $\text{SL}(2n,\mathbb{R})$ by codimension $2$ projective subspaces, or pencils of quadrics. In particular we show that if such a smooth fibration is…

We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.

Questions related to Brauer-Manin obstructions to the Hasse principle and weak approximation for homogeneous spaces of tori over a number field are well-studied, generally using arithmetic duality theorems, starting with works of Sansuc and…

We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the \'etale Brauer-Manin obstruction. We also give simple examples of threefolds with the same…

We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…

We describe descent on families of torsors of a constant torus. A recent result of Browning and Matthiesen then implies that the Brauer--Manin obstruction controls the Hasse principle and weak approximation when the ground field is the…