Good reduction of algebraic groups and flag varieties

Loop Groups and Their Flag Varieties

1. Reductive groups over local fields 1 1.1. Reductive groups over a field 1 1.2. The apartment of a reductive group over a local field 4 1.3. The existence of valuations of a root datum 12 1.4. The Bruhat-Tits group schemes 17 2. Loop groups 24 2.1. Definition of loop groups 24 2.2. The loop group of Ga and Gm 27 2.3. The loop groups of tori 30 2.4. Subgroups of LG 33 2.5. Integral models of L...

Good reduction of abelian varieties

ADJOINT SPACES AND FLAG VARIETIES OF p-COMPACT GROUPS

For a compact Lie group G with maximal torus T, Pittie and Smith showed that the flag variety G/T is always a stably framed boundary. We generalize this to the category of p-compact groups, where the geometric argument is replaced by a homotopy theoretic argument showing that the class in the stable homotopy groups of spheres represented by G/T is trivial, even G-equivariantly. As an applicatio...

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...

Jordan Groups and Automorphism Groups of Algebraic Varieties

The first section of this paper is focused on Jordan groups in abstract setting, the second on that in the settings of automorphisms groups and groups of birational self-maps of algebraic varieties. The appendix contains formulations of some open problems and the relevant comments. MSC 2010: 20E07, 14E07