The Manin Conjecture in Dimension 2
نویسنده
چکیده
منابع مشابه
Vojta’s Conjecture Implies the Batyrev-manin Conjecture for K3 Surfaces
Vojta’s Conjectures are well known to imply a wide range of results, known and unknown, in arithmetic geometry. In this paper, we add to the list by proving that they imply that rational points tend to repel each other on algebraic varieties with nonnegative Kodaira dimension. We use this to deduce, from Vojta’s Conjectures, conjectures of Batyrev-Manin and Manin on the distribution of rational...
متن کاملRelative Manin-Mumford for semi-abelian surfaces
We show that Ribet sections are the only obstruction to the validity of the relative Manin-Mumford conjecture for one dimensional families of semi-abelian surfaces. Applications include special cases of the Zilber-Pink conjecture for curves in a mixed Shimura variety of dimension four, as well as the study of polynomial Pell equations with non-separable discriminants.
متن کاملA short proof of the maximum conjecture in CR dimension one
In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
متن کاملA reduction of the Batyrev-Manin Conjecture for Kummer Surfaces
Let V be a K3 surface defined over a number field k. The BatyrevManin conjecture for V states that for every nonempty open subset U of V , there exists a finite set ZU of accumulating rational curves such that the density of rational points on U − ZU is strictly less than the density of rational points on ZU . Thus, the set of rational points of V conjecturally admits a stratification correspon...
متن کاملO-minimality and the André-Oort conjecture for C
We give an unconditional proof of the André-Oort conjecture for arbitrary products of modular curves. We establish two generalizations. The first includes the Manin-Mumford conjecture for arbitrary products of elliptic curves defined over Q as well as Lang’s conjecture for torsion points in powers of the multiplicative group. The second includes the Manin-Mumford conjecture for abelian varietie...
متن کامل