Brauer equivalence in a homogeneous space with connected stabilizer

Brauer Equivalence in a Homogeneous Space with Connected Stabilizer

Let G be a simply connected algebraic group over a field k of characteristic 0, H a connected k-subgroup of G, X = H\G. When k is a local field or a number field, we compute the set of Brauer equivalence classes in X(k). 0. Introduction In this note we investigate the Brauer equivalence in a homogeneous space X = H\G, where G is a simply connected algebraic group over a local field or a number ...

The Brauer–manin Obstructions for Homogeneous Spaces with Connected or Abelian Stabilizer

In this paper we prove that for a homogeneous space of a connected algebraic group with connected stabilizer and for a homogeneous space of a simply connected group with abelian stabilizer, the Brauer–Manin obstructions to the Hasse principle and weak approximation are the only ones. More precisely, let X be an algebraic variety over a number field k. The variety X is called a counter-example t...

Countable connected-homogeneous graphs

A graph is connected-homogeneous if any isomorphism between finite connected induced subgraphs extends to an automorphism of the graph. In this paper we classify the countably infinite connectedhomogeneous graphs. We prove that if Γ is connected countably infinite and connected-homogeneous then Γ is isomorphic to one of: Lachlan and Woodrow’s ultrahomogeneous graphs; the generic bipartite graph...

Locally-finite connected-homogeneous digraphs

Homogeneous Countable Connected Hausdorff Spaces

In 1925, P. Urysohn gave an example of a countable connected Hausdorff space [4]. Other examples have been contributed by R. Bing [l], M. Brown [2], and E. Hewitt [3]. Relatively few of the properties of such spaces have been examined. In this paper the question of homogeneity is studied. Theorem I shows that there exists a bihomogeneous countable connected Hausdorff space. Theorems II and III ...