44 citations · 170 across the 11 of their papers we have counts for
7 papers · 1 filter
Very strong approximation for certain algebraic varieties
Qing Liu, Fei Xu
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…
Hypersurfaces in projective schemes and a moving lemma
Ofer Gabber, Qing Liu, Dino Lorenzini
Let X/S be a quasi-projective morphism over an affine base. We develop in this article a technique for proving the existence of closed subschemes H/S of X/S with various favorable…
Néron models of algebraic curves
Qing Liu, Jilong Tong
Let S be a Dedekind scheme with field of functions K. We show that if X_K is a smooth connected proper curve of positive genus over K, then it admits a Néron model over S, i.e., a…
The index of an algebraic variety
Ofer Gabber, Qing Liu, Dino Lorenzini
Let K be the field of fractions of a Henselian discrete valuation ring O_K. Let X_K/K be a smooth proper geometrically connected scheme admitting a regular model X/O_K. We show tha…
Congruences of models of elliptic curves
Qing Liu, Huajun Lu
Let O_K be a discrete valuation ring with field of fractions K and perfect residue field. Let E be an elliptic curve over K, let L/K be a finite Galois extension and let O_L be the…
Stable reduction of finite covers of curves
Qing Liu
Let K be the function field of a connected regular scheme S of dimension 1, and let f : X -> Y be a finite cover of projective smooth and geometrically connected curves over K with…
Rational points of the group of components of a Neron model
Siegfried Bosch, Qing Liu
Let A_K be an abelian variety over a discrete valuation field K. Let A be the Neron model of A_K over the ring of integers O_K of K and A_k its special fibre. We study the set of r…