Results 11 to 20 of about 200 (50)
Counting integral points in certain homogeneous spaces [PDF]
, 2016 a
Wei, D., Xu, F.
core +1 more source
Strong approximation and descent [PDF]
, 2014 We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t)=N_{K/k}(z): firstly for quartic extensions of number fields K/k and quadratic polynomials P(t) in one ...
Derenthal, Ulrich, Wei, Dasheng
core +4 more sources
Boundedness of the p-primary torsion of the Brauer group of products of varieties
Forum of Mathematics, SigmaLet k be a field finitely generated over its prime subfield. We prove that the quotient of the Brauer group of a product of varieties over k by the sum of the images of the Brauer groups of factors has finite exponent.
Alexei Skorobogatov, Alexander Petrov
doaj +1 more source
Vanishing of Brauer groups of moduli stacks of stable curves
Forum of Mathematics, SigmaWe show that the cohomological Brauer groups of the moduli stacks of stable genus g curves over the integers and an algebraic closure of the rational numbers vanish for any $g\geq 2$ .
Sebastian Bartling, Kazuhiro Ito
doaj +1 more source
Bad reduction of the Brauer-Manin obstruction [PDF]
, 2015 We relate the Brauer group of a smooth variety over a p-adic field to the geometry of the special fibre of a regular model, using the purity theorem in \'etale cohomology. As an illustration, we describe how the Brauer group of a smooth del Pezzo surface
Bright, Martin
core +3 more sources
On the Brauer-Manin obstruction for degree four del Pezzo surfaces
, 2015 We show that, for every integer $1 \leq d \leq 4$ and every finite set $S$ of places, there exists a degree $d$ del Pezzo surface $X$ over ${\mathbb Q}$ such that ${\rm Br}(X)/{\rm Br}({\mathbb Q}) \cong {\mathbb Z}/2{\mathbb Z}$ and the Brauer-Manin ...
Jahnel, Jörg, Schindler, Damaris
core +1 more source
On the Brauer group of diagonal quartic surfaces
, 2011 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.
Ieronymou, Evis +2 more
core +1 more source
Integral Points for Multi-norm Tori
, 2012 We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of principle homogeneous spaces of multi-norm tori. Several explicit examples are provided.Comment: 25 pages.
Wei, Dasheng, Xu, Fei
core +1 more source
Zero-cycles on varieties over p-adic fields and Brauer groups
, 2014 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.
Saito, Shuji, Sato, Kanetomo
core +1 more source
An elementary proof of Hilbert's theorem on ternary quartics [PDF]
, 2010 In 1888, Hilbert proved that every non-negative quartic form f=f(x,y,z) with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and used advanced methods from topology and algebraic geometry.
Pfister, Albrecht, Scheiderer, Claus
core