EuDML | Browse

Let $K$ be a number field, and suppose $λ (x, t) \in K [x, t]$ is irreducible over $K (t)$ . Using algebraic geometry and group theory, we describe conditions under which the $K$ -exceptional set of $λ$ , i.e. the set of $α \in K$ for which the specialized polynomial $λ (x, α)$ is $K$ -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed $n \geq 10$ , all but finitely many $K$ -specializations of the degree $n$ generalized Laguerre polynomial $L_{n}^{(t)} (x)$ are $K$ -irreducible and have Galois group $S_{n}$ . Second, we study specializations...

This note gives a survey of some recent results on the stable reduction of covers of the projective line branched at three points.

Currently displaying 1 – 20 of 26

Page 1 Next

Displaying 1 – 20 of 26

Schottky uniformization theory on Riemann surfaces and Mumford curves of infinite genus.

Série de Poincaré pour certaines courbes

Singular moduli and supersingular moduli of Drinfeld modules.

Solving algebraic equations in roots of unity.

Some elliptic function identities

Some examples of torsion in the Griffiths group.

Some p-adic Galois Representations for Curves in Characteristic p.

Some Results on the Mordell-Weil Group of the Jacobian of the Fermat Curve.

Some stability properties of Teichmüller modular function fields with pro-l weight structures.

Special values of $L$ -functions attached to $X_{1} (N)$

Specializations of one-parameter families of polynomials

Stable maps of curves.

Stable Reduction and Uniformization of Abelian Varieties I.

Stable reduction of Fermat curves and Jacobi sum Hecke characters.

Stable reduction of three point covers

Stable vector bundles and the frobenius morphism

Stickelberger Ideals.

Sur des hauteurs alternatives. I.

Sur la conjecture de Birch-Swinnerton Dyer

Sur la formule de Deuring-Safarevic et un résultat de Nakajima.

Currently displaying 1 – 20 of 26