1,400 research outputs found
On the frequency of algebraic Brauer classes on certain log K3 surfaces
Given systems of two (inhomogeneous) quadratic equations in four variables,
it is known that the Hasse principle for integral points may fail. Sometimes
this failure can be explained by some integral Brauer-Manin obstruction. We
study the existence of a non-trivial algebraic part of the Brauer group for a
family of such systems and show that the failure of the integral Hasse
principle due to an algebraic Brauer-Manin obstruction is rare, as for a
generic choice of a system the algebraic part of the Brauer-group is trivial.
We use resolvent constructions to give quantitative upper bounds on the number
of exceptions.Comment: 13 page
On the Brauer-Manin obstruction for degree four del Pezzo surfaces
We show that, for every integer and every finite set of
places, there exists a degree del Pezzo surface over such
that and the
Brauer-Manin obstruction works exactly at the places in . For , we
prove that in all cases, with the exception of , this surface
may be chosen diagonalizably over
On the number of certain Del Pezzo surfaces of degree four violating the Hasse principle
We give an asymptotic expansion for the density of del Pezzo surfaces of
degree four in a certain Birch Swinnerton-Dyer family violating the Hasse
principle due to a Brauer-Manin obstruction. Under the assumption of Schinzel's
hypothesis and the finiteness of Tate-Shafarevich groups for elliptic curves,
we obtain an asymptotic formula for the number of all del Pezzo surfaces in the
family, which violate the Hasse principle.Comment: 27 page
On the algebraic Brauer classes on open degree four del Pezzo surfaces
We study the algebraic Brauer classes on open del Pezzo surfaces of degree
. I.e., on the complements of geometrically irreducible hyperplane sections
of del Pezzo surfaces of degree . We show that the -torsion part is
generated by classes of two different types. Moreover, there are two types of
-torsion classes. For each type, we discuss methods for the evaluation of
such a class at a rational point over a -adic field
Del Pezzo surfaces of degree four violating the Hasse principle are Zariski dense in the moduli scheme
We show that, over every number field, the degree four del Pezzo surfaces
that violate the Hasse principle are Zariski dense in the moduli scheme.Comment: 21 page
Symbolic struggles over solidarity in times of crisis: trade unions, civil society actors and the political far right in Austria
As a consequence of the recent financial and economic crisis, social cohesion
and integration are in jeopardy all over Europe. In this context, scholars also
speak of decreasing solidarity, which is defined as a normative obligation to
help each other and to make sacrifices to reach common goals. By taking the
empirical example of Austria, we argue that the meaning of solidarity is
increasingly being contested. Various collective actors such as trade unions,
civil society actors, but also right-wing populist parties are engaged in
symbolic struggles over solidarity. To show this, we examine the different
concepts and foundations of solidarity and analyse where and why they
conflict with each other, referring to recent debates on political issues, such
as the needs-based minimum benefit system and the access to the labour
market for refugees
- …