The theory of elliptic curves is distinguished by its long history and by the diversity of the
methods that have been used in its study. This book treats the arithmetic theory of elliptic …

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag,
1986), I observed that" the theory of elliptic curves is rich, varied, and amazingly vast," and …

The second edition builds on the first in several ways. There are three new chapters which
survey recent directions and extensions of the theory, and there are two new appendices …

In this chapter, we give the definition of Mordell–Weil lattice (in Sect. 6.5). First, we bring
together the concepts from Chaps. 4 and 5 in order to gain a better understanding of the …

In this paper we will generalize these examples to construct a canonical height on an
arbitrary variety V possessing a morphism~: VV and a divisor class q which is an eigenclass …

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Menu Find a journal Publish with us Track your research Search Cart Book cover Mordell–Weil …

Consider a smooth, geometrically irreducible, projective curve of genus g≥2 defined over a
number field of degree d≥1. It has at most finitely many rational points by the Mordell …

The article discusses the intersection of a curve with the variable algebraic subgroups of
multiplicative groups. It indicates the theorem that the sparse set alluded to is actually finite …

Let K/k be an extension of fields, and assume that it is primary: the algebraic closure of k in K
is purely inseparable over k. The most interesting case in practice is when K/k is a regular …

In this paper, we establish a theory of adelic line bundles over quasi-projective varieties over
finitely generated fields. Besides definitions of adelic line bundles, we consider their …