Some product formulas for theta functions in one and two variables
Some remarks on almost rational torsion points
For a commutative algebraic group over a perfect field , Ribet defined the set of almost rational torsion points of over . For positive integers , we show there is an integer such that for all tori of dimension at most over number fields of degree at most , . We show the corresponding result for abelian varieties with complex multiplication, and under an additional hypothesis, for elliptic curves without complex multiplication. Finally, we show that except for an explicit finite...
Some simple elliptic surfaces of genus zero.
Some special curves of genus 5
Sommes de Dedekind elliptiques et formes de Jacobi
À partir des formes de Jacobi , on construit une somme de Dedekind elliptique. On obtient ainsi un analogue elliptique aux sommes multiples de Dedekind construites à partir des fonctions cotangentes, étudiées par D. Zagier. En outre, on établit une loi de réciprocité satisfaite par ces nouvelles sommes. Par une procédure de limite, on peut retrouver la loi de réciprocité remplie par les sommes multiples de Dedekind classiques. D’autre part, en les spécialisant en des paramètres de points de 2- division,...
Special values of Hilbert modular functions.
Recently, Baily has established new foundation for complex multiplication in the context of Hilbert modular functions; see [1]-[4]. However, in his treatment there is a restriction on the class of CM-points treated. Namely, the order of complex multiplications associated to the point must be the maximal order in its quotient field. The purpose of this paper is two-fold: (1) to remove the restriction just mentioned; (2) to recover a result of Tate on the conjugates of CM-points by arbitrary Galois...
Specialization of endomorphism rings of abelian varieties
Specialization of the -adic polylogarithm to -th power roots of unity.
Specializations of one-parameter families of polynomials
Let be a number field, and suppose is irreducible over . Using algebraic geometry and group theory, we describe conditions under which the -exceptional set of , i.e. the set of for which the specialized polynomial is -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed , all but finitely many -specializations of the degree generalized Laguerre polynomial are -irreducible and have Galois group . Second, we study specializations...
Stable maps of curves.
Stable reduction of three point covers
This note gives a survey of some recent results on the stable reduction of covers of the projective line branched at three points.
Standard relations of multiple polylogarithm values at roots of unity.
Stark units and Kolyvagin's "Euler systems".
Stark–Heegner points on modular jacobians
Stickelberger elements in function fields
Strong approximation for the total space of certain quadric fibrations
Structure de torsion des courbes elliptiques sur les corps quadratiques
Structures galoisiennes et courbes elliptiques
Studying the growth of Mordell-Weil.
Subfields of the function field of the Deligne-Lusztig curve of Ree type