相关论文: The \'etale Brauer-Manin obstruction to strong app…

For a homogeneous space X (not necessarily principal) of a connected algebraic group G (not necessarily linear) over a number field k, we prove a theorem of strong approximation for the adelic points of X in the Brauer-Manin set. Namely,…

We reduce the question about whether the Brauer-Manin obstruction to weak approximation for homogeneous spaces is the only obstruction to the "simpler" question of the particular case of homogeneous spaces of $\mathrm{SL}_n$ with finite…

For a homogeneous space $X$ over a number field $k$, the Brauer-Manin obstruction has been used to study strong approximation for $X$ away from a finite set $S$ of places, and known results state that $X(k)$ is dense in the omitting-$S$…

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 study the strong approximation for classifying stacks $BG$, where $G$ is a linear algebraic group over a number field $k$. More specifically, we prove that the \'etale Brauer-Manin obstruction is the only obstruction to strong…

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…

Strong approximation with Brauer-Manin obstruction is established for smooth varieties containing a connected linear algebraic group with a compatible action.

We prove some new cases of real appoximation for homogeneous spaces with finite stabilizers and describe the state of the art around this question, giving proofs that are well-known to experts but that, to our knowledge, cannot be found in…

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a…

Let $k$ be a number field. We construct homogeneous spaces of $SL_{n,k}$ with finite nilpotent non-abelian stabilizers for which the Brauer-Manin obstruction does not explain the failure of strong approximation (resp. the failure of the…

Let X be a homogeneous space of a quasi-trivial k-group G, with geometric stabilizer H, over a number field k. We prove that under certain conditions on the character group of H, certain algebraic Brauer-Manin obstructions to the Hasse…

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…

Let $G$ be a connected linear algebraic group over a number field. Let $U \hookrightarrow X$ be a $G$-equivariant open embedding of a $G$-homogeneous space with connected stabilizers into a smooth $G$-variety. We prove that $X$ satisfies…

We give formulas for calculating the unramified Brauer group of a homogeneous space $X$ of a semisimple simply connected group $G$ with finite geometric stabilizer $\bar F$ over a wide family of fields of characteristic 0. When $k$ is a…

We prove that the Brauer-Manin obstruction is the only obstruction to the Hasse principle for homogeneous spaces with nilpotent stabilizer. We thus generalize recent results by Harpaz and Wittenberg on finite "hyper-solvable" stabilizers.…

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…

We provide an algorithm for calculating the unramified Brauer group of a homogeneous space $X$ of a semi-simple simply connected group $H$ with finite geometric stabiliser over any field of characteristic 0. When $k$ is a number field, we…

Let X be a homogeneous space of a connected linear algebraic group G' over a number field k, containing a k-point x. Assume that the stabilizer of x in G' is connected. Using the notion of a quasi-trivial group, recently introduced by…

We show that the Brauer-Manin obstruction is the only obstruction to strong approximation for all stacky curves over global fields with finite abelian fundamental groups. This includes all stacky curves of genus $g = \frac{1}{2}$, thus…

We study an analogue of the Brauer-Manin obstruction to the local-global principle for embedding problems over global fields. We will prove the analogues of several fundamental structural results. In particular we show that the (algebraic)…