On the classification of 3-dimensional non-associative division algebras over p-adic fields

INDECOMPOSABLE AND NONCROSSED PRODUCT DIVISION ALGEBRAS OVER FUNCTION FIELDS OF SMOOTH p-ADIC CURVES

We construct indecomposable and noncrossed product division algebras over function fields of smooth curves X over Zp. This is done by defining an index preserving morphism s : Br(K̂(X)) → Br(K(X)) which splits res : Br(K(X)) → Br(K̂(X)), where K̂(X) is the completion of K(X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over K̂(X).

On the Classification of Four-Dimensional Quadratic Division Algebras over Square-Ordered Fields

A square-ordered field, also called Hilbert field of type (A), is understood to be an ordered field all of whose positive elements are squares. The problem of classifying, up to isomorphism, all 4-dimensional quadratic division algebras over a square-ordered field k is shown to be equivalent to the problem of finding normal forms for all pairs (X, Y ) of 3× 3-matrices over k, X being antisymmet...

Hecke Algebras of Classical Groups over p-adic Fields II

In the previous part of this paper, we constructed a large family of Hecke algebras on some classical groups G de¢ned over p-adic ¢elds in order to understand their admissible representations. EachHecke algebra is associated to a pair …JS; rS†of an open compact subgroup JS and its irreducible representation rSwhich is constructed fromgiven dataS ˆ …G;P0 0; R†. Here, G is a semisimple element in...

Classification of two dimensional trianguline representations of p-adic fields

The aim of this paper is to classify two dimensional trianguline representations of padic fields. This is a generalization of a result of Colmez who classified two dimensional trianguline representations of Gal(Q̄p/Qp) by using (φ,Γ)-modules over Robba ring. In this paper, we classify two dimensional trianguline representations of Gal(K̄/K) for general p-adic field K by using B-pairs defined by B...

Triangulaizability of Algebras Over Division Rings