The purpose of this article is to prove that Gersten’s conjecture for a commutative discrete valuation ring is true. Combining with the result of [GL87], we learn that Gersten’s conjecture is true if the ring is a commutative regular local, smooth over a commutative discrete valuation ring.

Given a place between two fields, the isotropy behaviour of Azumaya algebras with involution over the valuation ring corresponding to the place is studied. In particular, it is shown that isotropic right ideals specialise in an appropriate way. The treatment is characteristic free, and it provides a natural analogue to the existing specialisation theory for non-singular symmetric bilinear forms...

In the case that X,Y are projective, nonsingular curves and φ is nonconstant, we already know that φ is necessarily surjective, but we will prove (more accurately, sketch a proof of) a much stronger result. From now on, for convenience, when we speak of the local ring of a nonsingular curve as being a discrete valuation ring, we assume that the valuation is normalized so that there is an elemen...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.