Algebraic vector bundles over real algebraic varieties

Vector bundles over algebraic curves

Stable Real Algebraic Vector Bundles over a Klein Bottle

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over X .

Analytic Cycles and Vector Bundles on Non-Compact Algebraic Varieties*

A. Orders of Growth on Algebraic Varieties . . . . . . . . . . . 4 w 1. Review of the Classical Theory . . . . . . . . . . . . . 4 w 2. Generalization to Algebraic Varieties . . . . . . . . . . . 6 w 3. Exhaustion Functions and K~ihler Metrics on Special Affine Varieties . . . . . . . . . . . . . . . . . . . . . . . 9 84. Order of Growth of Analytic Sets . . . . . . . . . . . . 13 w 5. Order of...

Representations of Algebraic Groups and Principal Bundles on Algebraic Varieties

In this talk we discuss the relations between representations of algebraic groups and principal bundles on algebraic varieties, especially in characteristic p. We quickly review the notions of stable and semistable vector bundles and principal G-bundles , where G is any semisimple group. We define the notion of a low height representation in characteristic p and outline a proof of the theorem t...

Algebraic Varieties over Small Fields

— We study curves and their Jacobians over F̄p and Q̄, and discuss applications to rational connectivity over these fields. We introduce certain dynamical systems on P, induced by translates by torsion points on elliptic curves, and study fields related to these systems.