Mass formula of division algebras over global function fields

Triangulaizability of Algebras Over Division Rings

Nicely semiramified division algebras over Henselian fields

We recall that a nicely semiramified division algebra is defined to be a defectless finitedimensional valued central division algebra D over a field E with inertial and totally ramified radical-type (TRRT) maximal subfields [7, Definition, page 149]. Equivalent statements to this definition were given in [7, Theorem 4.4] when the field E is Henselian. These division algebras, as claimed in [7, ...

Kummer subfields of tame division algebras over Henselian valued fields

By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and Corollary 2.12]. We prove also that if D is a tame semiramified division algebra of prime power degree p over E such that p 6= char(Ē) and rk(ΓD/ΓF ) ≥ 3 [re...

triangulaizability of algebras over division rings

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).