Related papers: Brauer groups of certain affine cubic surfaces

We classify finite groups acting by birational transformations of a non-trivial Severi--Brauer surface over a field of characteristc zero that are not conjugate to subgroups of the automorphism group. Also, we show that the automorphism…

Let $k$ be a field and $X/k$ be a smooth quasiprojective orbifold. Let $X\to \underline{X}$ be its coarse moduli space. In this paper we study the Brauer group of $X$ and compare it with the Brauer group of the smooth locus of…

Building upon our arithmetic duality theorems for 1-motives, we prove that the Manin obstruction related to a finite subquotient $\Be (X)$ of the Brauer group is the only obstruction to the Hasse principle for rational points on torsors…

Embeddings of maximal tori into classical groups over global fields of characteristic not 2 are the subject matter of several recent papers, with special attention to the Hasse principle. The present paper gives necessary and sufficient…

An integer may be represented by a quadratic form over each ring of p-adic integers and over the reals without being represented by this quadratic form over the integers. More generally, such failure of a local-global principle may occur…

The class in the Brauer group of a quaternion algebra over a field is 2-torsion. We study the following question: Which 2-torsion elements of the Brauer group of a complex function field are representable by quaternion algebras? Using…

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…

We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over the field of complex numbers this is an elementary abelian 2-group with an explicit upper…

Let G be a connected linear algebraic group over a number field k. We establish an exact sequence describing the closure of the group G(k) of rational points of G in the group of adelic points of G. This exact sequence describes the defect…

Let k be a number field and X a smooth projective k-variety. In this paper, we study the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points on X within the adelic points.…

We develop different formulas of algebraic and/or arithmetic nature allowing an explicit calculation, both over a finite field and over a field of characteristic 0, of the algebraic part of the unramified Brauer group of a homogeneous space…

We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over Q to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of Q.…

Using Maruyama's theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree…

We study effective bounds for Brauer groups of Kummer surfaces associated to the Jacobians of curves of genus $2$ defined over number fields.

We construct an Enriques surface X over Q with empty \'etale-Brauer set (and hence no rational points) for which there is no algebraic Brauer-Manin obstruction to the Hasse principle. In addition, if there is a transcendental obstruction on…

For a smooth and geometrically irreducible variety X over a field k, the quotient of the absolute Galois group G_{k(X)} by the commutator subgroup of G_{\bar k(X)} projects onto G_k. We investigate the sections of this projection. We show…

We construct moduli spaces of complex affine and dilation surfaces. Using ideas of Veech, we show that the the moduli space of affine surfaces with fixed genus and with cone points of fixed complex order is a holomorphic affine bundle over…

We fit the Brauer group of a $\mu_r$-gerbe over a (possibly arbitrarily singular) stacky curve into an exact sequence and give characterizations for when it is short exact and conditions for when it splits. We also give a precise formula…

In this paper we investigate the quantity of diagonal quartic surfaces $a_0 X_0^4 + a_1 X_1^4 + a_2 X_2^4 +a_3 X_3^4 = 0$ which have a Brauer-Manin obstruction to the Hasse principle. We are able to find an asymptotic formula for the…

We study arithmetic of the algebraic varieties defined over number fields by applying Lagrange interpolation to fibrations. Assuming the finiteness of the Tate-Shafarevich group of a certain elliptic curve, we show, for Ch\^atelet surface…