On the class group of affinoid spaces
On the closed subfields of [...] Q ¯ p
Let p be a prime number, and let [...] Q¯ p be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.
On the Completion of a Valuation Ring.
On the dimension of the space of ℝ-places of certain rational function fields
We prove that for every n ∈ ℕ the space M(K(x 1, …, x n) of ℝ-places of the field K(x 1, …, x n) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x 1, …, x n)) ≤ n. For n = 2 the space M(K(x 1, x 2)) has covering and integral dimensions dimM(K(x 1, x 2)) = dimℤ M(K(x 1, x 2)) = 2 and the cohomological dimension dimG M(K(x 1, x 2)) = 1 for any Abelian 2-divisible coefficient group G.
On the extension of a valuation on a field to . - II
On the Extension of Real Places
On the extension of valuations on a field to . - I
On the irreducible factors of a polynomial over a valued field
We explicitly provide numbers , such that each irreducible factor of a polynomial with integer coefficients has a degree greater than or equal to and can have at most irreducible factors over the field of rational numbers. Moreover, we prove our result in a more general setup for polynomials with coefficients from the valuation ring of an arbitrary valued field.
On the Jacobian conjecture and the configurations of roots.
On the Local Skolem Property.
On the main invariant of an element over a local field.
On the model companion for e-fold p-adically valued fields.
On the Nonflatness of Analytic Tensor Product.
On the seperation of basic semialgebraic sets by polynomials.
On the structure of compact subsets of ℂₚ
On the theory of cuts in ordered fields.
On tolerant valuation rings.
On topological fields
On two types of complete discrete valuation fields
On valuations of nearfields