Etale cohomology of henselian rings and cohomology of abstract Riemann surfaces of fields.
Etale coverings of a Mumford curve
Let the field be complete w.r.t. a non-archimedean valuation. Let be a Mumford curve, i.e. the irreducible components of the stable reduction of have genus 0. The abelian etale coverings of are constructed using the analytic uniformization and the theta-functions on . For a local field one rediscovers . Frey’s description of the maximal abelian unramified extension of the field of rational functions of .
Étale Galois covers of affine smooth cuves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture.
Étude de la courbe elliptique et monogénéité de certains anneaux d’entiers
Étude des intégrales abéliennes de troisième espèce
Étude sur les relations algébriques entre les fonctions hyperelliptiques de genre 3
Euclidean algorithm and Kummer covers with many points.
Euler characteristics of moduli spaces of curves
Let be the moduli space of -pointed Riemann surfaces of genus . Denote by the Deligne-Mumford compactification of . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of for any and such that .
Euler's concordant forms
Exceptional linear systems on curves on Del Pezzo surfaces.
Exemples de courbes de P3 à fibré normal semi-stable, stable.
Existence de faisceaux réflexifs de rang deux sur à bonne cohomologie
Existence, decomposition, and limits of certain Weierstrass points.
Existence of coherent systems of rank two and dimension four.
We show that the moduli space of coherent systems of rank two and dimension four on a generic curve of genus at least two is non-empty for any value of the parameter when the Brill-Noether number is at least one and the degree is odd or when the Brill-Noether number is at least ve and the degree is even. In all these cases there is one component of the moduli space of coherent systems of the expected dimension. The case of rank two and dimension four is particularly relevant as it is the rst case...
Experimental study of the rank of families of elliptic curves over . (Étude expérimentale du rang de familles de courbes elliptiques sur .)
Explicit 4-descents on an elliptic curve
Explicit construction of a global uniformization for an algebraic correspondence.
Explicit descent for Jacobians of cyclic coevers of the projective line.
Explicit form of the modular equation.
Explicit moduli for curves of genus 2 with real multiplication by ℚ(√5)
1. Motivation. Let J₀(N) denote the Jacobian of the modular curve X₀(N) parametrizing pairs of N-isogenous elliptic curves. The simple factors of J₀(N) have real multiplication, that is to say that the endomorphism ring of a simple factor A contains an order in a totally real number field of degree dim A. We shall sometimes abbreviate "real multiplication" to "RM" and say that A has maximal RM by the totally real field F if A has an action of the full ring of integers of F. We say that a...