相关论文: Compatibility of weak approximation for zero-cycle…

We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.

For smooth open toric varieties, we establish strong approximation off infinity with Brauer-Manin obstruction.

A conjecture of Colliot-Th\'{e}l\`{e}ne predicts that for a smooth projective variety $X$ over a finite extension $k$ of $\mathbb{Q}_p$ the kernel of the Albanese map $\text{CH}_0(X)^{\text{deg}=0}\to Alb_X(k)$ is the direct sum of a…

Let $X$ be a $K3$ surface over a $p$-adic field $k$ such that for some abelian surface $A$ isogenous to a product of two elliptic curves, there is an isomorphism over the algebraic closure of $k$ between $X$ and the Kummer surface…

Recently Dasheng Wei proved that the Brauer-Manin obstruction is the only obstruction to the Hasse principle for 0-cycles of degree 1 on some fibrations over the projective line defined by bi-cyclic normic equations. In the present paper,…

We investigate the question of whether the existence of a family of local zero-cycles of degree $d$ orthogonal to the Brauer group implies the non-emptiness of the Brauer-Manin set for certain varieties. We provide various examples of…

Given a family of varieties $X\to \mathbb{P}^n$ over a number field $k$, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for $100\%$ of the fibres which are everywhere locally soluble.

We study a conjecture, due to Voisin, on 0-cycles on varieties with $p_g=1$. Using Kimura's finite dimensional motives and recent results of Vial's on the refined (Chow-)K\"unneth decomposition, we provide a general criterion for Calabi-Yau…

In this paper, we study the Brauer-Manin pairing of smooth proper varieties over local fields, and determine the $p$-adic part of the kernel of one side. We also compute the $A_0$ of a potentially rational surface which splits over a wildly…

Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over number fields were proposed by Colliot-Th\'el\`ene, Sansuc, Kato and Saito in the 1980's. We prove that these conjectures are compatible with…

We report on our experiments and theoretical investigations concerning weak approximation and the transcendental Brauer-Manin obstruction for special Kummer surfaces.

We give a geometric criterion to check the validity of the integral Tate conjecture for one-cycles on a smooth projective variety that is separably rationally connected in codimension one, and to check that the Brauer-Manin obstruction is…

This is a survey of weak approximation over complex function fields, touching on the Koll'ar-Miyaoka-Mori theorem, places of good and bad reduction, the special case of rational surfaces, rationally simply connected varieties, and…

We provide a relation between Brauer-Manin obstruction and descent obstruction for torsors over open varieties under a connected linear algebraic group or a group of multiplicative type is given. Such a relation is further refined for…

For rational points on algebraic varieties defined over a number field $K$, we study the behavior of the property of weak approximation with Brauer-Manin obstruction under extension of the ground field. We construct K-varieties accompanied…

Let $X$ be a smooth projective variety over a number field, fibered over a curve, with geometrically integral fibers. We prove that, supposing the finiteness of $\sha(Jac(C))$, if the fibers over a generalised Hilbertian subset satisfy the…

We explore the connection between $K3$ categories and 0-cycles on holomorphic symplectic varieties. In this paper, we focus on Kuznetsov's noncommutative $K3$ category associated to a nonsingular cubic 4-fold. By introducing a filtration on…

For 0-cycles on a variety over a number field, we define an analogue of the classical descent set for rational points. This leads to, among other things, a definition of the \'etale-Brauer obstruction set for 0-cycles, which we show is…

In this article, we study obstructions to weak approximation for connected linear groups and homogeneous spaces with connected or abelian stabilizers over finite extensions of $\mathbb C((x,y))$ or function fields of curves over $\mathbb…

We study the Brauer-Manin obstruction to the Hasse principle and to weak approximation for 0-cycles on algebraic varieties that possess a fibration structure. The exactness of the local-to-global sequence $(E)$ of Chow groups of 0-cycles…