Related papers: Weak Approximation for Isotrivial Families

We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.

This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reduction. Our approach entails analyzing the rational connectivity of the smooth locus of…

This is a survey of weak approximation over complex function fields, touching on the Koll'ar-Miyaoka-Mori theorem, places of good and bad reduction, the special case of rational surfaces, rationally simply connected varieties, and…

We prove weak approximation for smooth cubic hypersurfaces of dimension at least 2 defined over the function field of a complex curve.

We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can…

We prove some triviality results for reduced Whitehead groups and reduced unitary Whitehead groups for division algebras over a henselian discrete valuation field whose residue field has virtual cohomological dimension or separable…

Let $k$ be a $d$-local field of characteristic 0, and let $K$ be the function field of a nice curve over $k$. We give a defect to weak approximation for reductive groups over $K$ using arithmetic dualities.

Let $K=k(C)$ be the function field of a curve over a field $k$ and let $X$ be a smooth, projective, separably rationally connected $K$-variety with $X(K)\neq\emptyset$. Under the assumption that $X$ admits a smooth projective model $\pi:…

Let X,Y be projective schemes over a discrete valuation ring R, where Y is generically smooth and g:X \to Y a surjective R-morphism such that g_*\mathcal{O}_X = \mathcal{O}_Y. We show that if the family X \to Spec(R) is isotrivial, then the…

In this short note we give a characterization of smooth projective varieties of Picard number one that are separably uniruled but not separably rationally connected. We also give a sufficient condition involving the torsion order and the…

This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…

In this paper we prove that a smooth family of canonically polarized manifolds parametrized by a special (in the sense of Campana) quasi-projective variety is isotrivial.

We present a new perspective on the weak approximation conjecture of Hassett and Tschinkel: formal sections of a rationally connected fibration over a curve can be approximated to arbitrary order by regular sections. The new approach…

We study weak approximation on rationally connected varieties under an assumption of strong approximation for a "simple" variety or under Schinzel's hypothesis. We also get some unconditional results.

In this paper, we point out that the definition of weak tracial approximation can be improved and strengthened. An example of weak tracial approximation is also provided.

We characterize having Borel isomorphism relation among some weakly minimal trivial theories, namely the examples of families of finite equivalence relations from recent joint work with Laskowski, and tame expansions of…

In this paper we study families of projective manifolds with good minimal models. After constructing a suitable moduli functor for polarized varieties with canonical singularities, we show that, if not birationally isotrivial, the base…

Campana introduced a notion of Campana rational connectedness for Campana orbifolds. Given a Campana fibration over a complex curve, we prove that a version of weak approximation for Campana sections holds at places of good reduction when…

We establish arithmetic duality theorems for short complexes associated to reductive groups over $p$-adic function fields. Using dualities, we deduce obstructions to weak approximation for certain reductive groups (especially quasi-split…

Let k be a number field. For a variety X over k that satisfies weak approximation with Brauer-Manin obstruction, we study the same property for smooth projective models of its symmetric products. Based on the same method, we also explore…