Elliptic curves with a rational point of finite order.
Elliptic curves with bounded ranks in function field towers
Elliptic Curves With Complex Multiplication and the Conjecture of Birch and Swinnerton-Dyer.
Elliptic Surface Singularities and Smoothings of Curves.
Elliptische Funktionenkörper mit schlechter Reduktion.
Embeddings of Curves.
Empilements de sphères
Endomorphisms of group schemes and rational points on curves
Endomorphisms of jacobian varieties of Fermat curves
Energy decay rates for solutions of Maxwell's system with a memory boundary condition
We consider the stabilization of Maxwell's equations with space variable coefficients in a bounded region with a smooth boundary, subject to dissipative boundary conditions of memory type on the boundary. Under suitable conditions on the domain and on the permeability and permittivity coefficients, we prove the exponential/polynomial decay of the energy. Our result is mainly based on the use of the multipliers method and the introduction of a suitable Lyapounov functional.
Entrelacs toriques itérés et intégrales associées à une courbe plane
Enumerative geometry of divisorial families of rational curves
We compute the number of irreducible rational curves of given degree with 1 tacnode in or 1 node in meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the number of rational plane curves of degree passing through given points and tangent to a given line. The method is ‘classical’, free of Quantum Cohomology.
Enumerative geometry of singular plane curves.
Équations différentielles -adiques et dégénérescence de groupes de Hodge
Equations of hyperelliptic modular curves
We compute, in a unified way, the equations of all hyperelliptic modular curves. The main tool is provided by a class of modular functions introduced by Newman in 1957. The method uses the action of the hyperelliptic involution on the cusps.
Equianalytic and equisingular families of curves on surfaces.
Equivalence of families of singular schemes on threefolds and on ruled fourfolds.
The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for families of...
Equivalences between elliptic curves and real quadratic congruence function fields
In 1994, the well-known Diffie-Hellman key exchange protocol was for the first time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number field. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function fields, whose set of reduced principal ideals has a similar infrastructure. As always, the security...
Equivariant counts of points of the moduli spaces of pointed hyperelliptic curves.
Equivariant Form of the Deuring-Safarevic Formula for Hasse-Witt Invariants.