Universal bounds on the torsion of elliptic curves
Universal covering spaces and fundamental groups in algebraic geometry as schemes
In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a fundamental group family from a universal cover, both of which are schemes. A geometric fiber of the fundamental group family (as a topological group) is canonically the étale fundamental group. The constructions apply to all connected quasicompact quasiseparated schemes. With different methods and hypotheses,...
Universal extensions and -adic periods of elliptic curves
Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves
Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.
Unramified nonspecial real space curves having many real branches and few ovals.
Let C ⊆ Pn be an unramified nonspecial real space curve having many real branches and few ovals. We show that C is a rational normal curve if n is even, and that C is an M-curve having no ovals if n is odd.
Unramified Skolem problems and unramified arithmetic Bertini theorems in positive characteristic.
Unterbündel maximalen Grades von Vektorbündeln auf algebraischen Kurven.
Untersuchungen über die Theilwerthe der Jacobischen Thetafunctionen und die im Gauss'schen Nachlasse mitgetheilten Beziehungen derselben
Určování nekonečně vzdálených prvků útvarů geometrických