Related papers: Descent on toric fibrations
We give an exposition of the formal aspects of deformation theory in the language of fibered categories, instead of the more traditional one of functors. The main concepts are that of tangent space to a deformation problem, obstruction…
For a family of varieties over a number field, we give conditions under which 100% of members have no Brauer-Manin obstruction to the Hasse principle.
For a quasi-projective smooth geometrically integral variety over a number field $k$, we prove that the iterated descent obstruction is equivalent to the descent obstruction. This generalizes a result of Skorobogatov, and this answers an…
We study the failure of the integral Hasse principle and strong approximation for Markoff surfaces, as studied by Ghosh and Sarnak, using the Brauer-Manin obstruction.
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)…
We prove the Hasse principle and weak approximation for varieties defined over number fields by the nonsingular intersection of pairs of quadratic forms in 8 variables. The argument develops work of Colliot-Thelene, Sansuc and…
Manin's conjecture predicts the distribution of rational points on Fano varieties. Using explicit parameterizations of rational points by integral points on universal torsors and lattice-point-counting techniques, it was proved for several…
This is an outline of work in progress concerning an algebro-geometric form of the Strominger-Yau-Zaslow conjecture. We introduce a limited type of degeneration of Calabi-Yau manifolds, which we call toric degenerations. For these, the…
In this paper, we study weak approximation with Brauer--Manin obstruction with respect to extensions of number fields. For any nontrivial extension $L/K,$ assuming a conjecture of M. Stoll, we prove that there exists a $K$-threefold…
In this paper we prove reducibility of classes of linear first order operators on tori by applying a generalization of Moser's theorem on straightening of vector fields on a torus. We consider vector fields which are a $C^\infty$…
Investigating a conjecture of Zannier, we study irreducible subvarieties of abelian schemes that dominate the base and contain a Zariski dense set of torsion points that lie on pairwise isogenous fibers. If everything is defined over the…
Draft version of a paper concerning an interpretation of the conditon (UA) in terms of descent with respect to the fibrations of points.
A reduction formula for the branching coefficients of tensor products of representations and more generally restrictions of representations of a semisimple group to a semisimple subgroup is proved in work by Knutson-Tao and Derksen-Weyman.…
We discuss various topics on degenerations and special Lagrangian torus fibrations of Calabi-Yau manifolds in the context of mirror symmetry. A particular emphasis is on Tyurin degenerations and the Doran-Harder-Thompson conjecture, which…
We develop an effective theory for biased tracers formulated at the level of the Boltzmann equation, providing a unified description of density and velocity bias. We introduce a general effective collision term in the tracer Boltzmann…
Let F be a global field. In this work, we show that the Brauer-Manin condition on adelic points for subvarieties of a torus T over F cuts out exactly the rational points, if either F is a function field or, if F is the field of rational…
The aim of this paper is to revisit the question of local-global principles for embeddings of \'etale algebras with involution into central simple algebras with involution over global fields of characteristic not 2. A necessary and…
In this work, we mainly concern the limiting behavior of the electromagnetic field of two species Vlasov-Maxwell-Botlzmann system in diffusive limits. As knudsen numbers goes to zero, the electric magnetic and magnetic field may perserve or…
Every function over the natural numbers has an infinite subdomain on which the function is non-decreasing. Motivated by a question of Dzhafarov and Schweber, we study the reverse mathematics of variants of this statement. It turns out that…
We consider the Navier-Stokes-Fourier system describing the motion of a compressible, viscous and heat-conducting fluid on a domain perforated by tiny holes. First, we identify a class of dissipative solutions to the Oberbeck-Boussinesq…