Basepoint freeness for nef and big line bundles in positive characteristic.
Beispiele dreidimensionaler Hilbertscher Modulmannigfaltigkeiten von allgemeinem Typ.
Beyond two criteria for supersingularity: coefficients of division polynomials
Let be a cubic, monic and separable polynomial over a field of characteristic and let be the elliptic curve given by . In this paper we prove that the coefficient at in the –th division polynomial of equals the coefficient at in . For elliptic curves over a finite field of characteristic , the first coefficient is zero if and only if 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.
Bogomolov instability of higher rank sheaves on surfaces in characteristic p.
Borne polynomiale pour le nombre de points rationnels des courbes
Soit un polynôme en deux variables, de degré et à coefficients entiers dans pour . Alors le nombre de zéros rationnels de est soit infini soit plus petit que . Nous montrons aussi une version plus générale sur les corps de nombres.
Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications
Boundary cohomology of Shimura varieties, II. Hodge theory at the boundary (Erratum).
Boundary cohomology of Shimura varieties. II. Hodge theory at the boundary.
Bounds for rational points on twists of constant hyperelliptic curves.
Bounds on polarizations of abelian varieties over finite fields.
Bruhat-Tits theory from Berkovich’s point of view. I. Realizations and compactifications of buildings
We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group over a suitable non-Archimedean field we define a map from the Bruhat-Tits building to the Berkovich analytic space associated with . Composing this map with the projection of to its flag varieties, we define a family of compactifications of . This generalizes results by Berkovich in the case of split groups. Moreover,...