For an o-minimal expansion R of a real closed field and a set V of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to V . This is an elementary extension S of R generated by all completions of all the residue fields of the V ∈ V , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings u...

We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discrete valuation rings. In order to prove these results we determine (using the theory of Breuil modules) when two finite flat group schemes G and H of order p over an arbitrarily tamely ramified discrete valuation ring ...

Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading monoid $G$. For each positive integer, the notions of graded-n-coherent module and are introduced. In this paper many results generalized from $n$-coherent rings to graded-$n$-coherent rings. last section, we provide necessary sufficient conditions for trivial extension graded-valuation ri...

We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discrete valuation rings. In order to prove these results we determine (using the theory of Breuil modules) when two finite flat group schemes G and H of order p over an arbitrarily tamely ramified discrete valuation ring ...

This work is a part of my research in the area of model theory. First we study a particular L-theory of rings whose models are called p-convexly valued domains (the first-order language L is the language of rings equipped with a linear divisibility predicate and predicates for the nth powers). It consists of a p-adic counterpart of Becker’s convexly oredered valuation rings. Then we are interes...

Given a generically finite local extension of valuation rings V ⊂ W $V \subset W$ , the question whether is localization finitely generated V-algebra significant for approaches to problem uniformization valuations using ramification theory. Hagen Knaf proposed characterization when essentially type over in terms classical invariants associated valuations. Knaf's conjecture has been verified imp...