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Nous dressons un rapide panorama de résultats allant dans le sens de la conjecture suivante : l’intersection d’une sous-variété $X$ d’une variété semi-abélienne $A$ et de l’union de tous les sous-groupes algébriques de $A$ de codimension au moins $dim X + 1$ n’est pas Zariski-dense dans $X$ dès que $X$ n’est pas contenue dans un sous-groupe algébrique strict de $A$ .

Basepoint freeness for nef and big line bundles in positive characteristic.

Keel, Seán (1999)

Annals of Mathematics. Second Series

Beispiele dreidimensionaler Hilbertscher Modulmannigfaltigkeiten von allgemeinem Typ.

Friedrich Wilhelm Knöller (1982)

Manuscripta mathematica

Beyond two criteria for supersingularity: coefficients of division polynomials

Christophe Debry (2014)

Journal de Théorie des Nombres de Bordeaux

Let $f (x)$ be a cubic, monic and separable polynomial over a field of characteristic $p \geq 3$ and let $E$ be the elliptic curve given by $y^{2} = f (x)$ . In this paper we prove that the coefficient at $x^{\frac{1}{2} p (p - 1)}$ in the $p$ –th division polynomial of $E$ equals the coefficient at $x^{p - 1}$ in $f {(x)}^{\frac{1}{2} (p - 1)}$ . For elliptic curves over a finite field of characteristic $p$ , the first coefficient is zero if and only if $E$ is supersingular, which by a classical criterion of Deuring (1941) is also equivalent to the vanishing of the second coefficient. So the zero loci...

Birational invariants in the case of prime characteristic.

D. Müller, P. Brückmann (1998)

Manuscripta mathematica

Bogomolov instability of higher rank sheaves on surfaces in characteristic p.

G. Megyesi (1995)

Mathematische Annalen

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