On the distribution of the Fₚ-points on an affine curve in r dimensions
On the division polynomials of elliptic curves.
On the elliptic logarithm method for elliptic Diophantine equations: reflections and an improvement.
On the equation
On the equation . (Sur l'équation .)
On the equation a³ + b³ⁿ = c²
We study coprime integer solutions to the equation a³ + b³ⁿ = c² using Galois representations and modular forms. This case represents perhaps the last natural family of generalized Fermat equations descended from spherical cases which is amenable to resolution using the so-called modular method. Our techniques involve an elaborate combination of ingredients, ranging from ℚ-curves and a delicate multi-Frey approach, to appeal to intricate image of inertia arguments.
On the Euler-Poincaré characteristics of finite dimensional -adic Galois representations
On the existence of dimension zero divisors in algebraic function fields defined over
On the existence of supersingular curves of given genus.
On the extendability of elliptic surfaces of rank two and higher
We study threefolds having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not hyperplane section of a locally complete intersection threefold and we give some conditions, for many embeddings...
On the ...-factor attached to motives.
On the finiteness of for motives associated to modular forms.
On the Fourier coefficients of modular forms. II.
On the generalized principal ideal theorem of complex multiplication
In the -th cyclotomic field a prime number, , the prime is totally ramified and the only ideal above is generated by , with the primitive -th root of unity . Moreover these numbers represent a norm coherent set, i.e. . It is the aim of this article to establish a similar result for the ray class field of conductor over an imaginary quadratic number field where is the power of a prime ideal in . Therefore the exponential function has to be replaced by a suitable elliptic function....
On the group orders of elliptic curves over finite fields
On the Hasse principle for Witt groups.
On the height constant for curves of genus two
On the height constant for curves of genus two, II
On the height of algebraic numbers with real conjugates
On the height of the Sylvester resultant.