On ramified complete discrete valuation rings

On Ramified Complete Discrete Valuation Rings

A Classification of Modules over Complete Discrete Valuation Rings

Complete fields and valuation rings

In order to make further progress in our investigation of finite extensions L/K of the fraction field K of a Dedekind domain A, and in particular, to determine the primes p of K that ramify in L, we introduce a new tool that allows us to “localize” fields. We have seen how useful it can be to localize the ring A at a prime ideal p: this yields a discrete valuation ring Ap, a principal ideal dom...

Integral Crystalline Cohomology over Very Ramified Valuation Rings

In this paper we intend to show how Fontaine’s comparison-theory ([Fo1], [Fo2]) between crystalline and p-adic étale cohomology can be extented to very ramified base rings. So far it had been developed either for Qp-coefficients, or Zp-coefficients if the base is unramified over the Witt-vectors (see [Fa2]). For example it states that for any p-adic discrete valuation-ring V there exists a ring...

Gersten’s conjecture for commutative discrete valuation rings

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.