On the Tate constant
On the theory of cuts in ordered fields.
On the Uniqueness of Real Closures and the Existence of Real Places
On the vanishing of Hochschild homology of locally complete intersections.
On the Various Bisection Methods Derived from Vincent’s Theorem
In 2000 A. Alesina and M. Galuzzi presented Vincent’s theorem “from a modern point of view” along with two new bisection methods derived from it, B and C. Their profound understanding of Vincent’s theorem is responsible for simplicity — the characteristic property of these two methods. In this paper we compare the performance of these two new bisection methods — i.e. the time they take, as well as the number of intervals they examine in order to isolate the real roots of polynomials — against that...
On the zeros of polynomials over arbitrary finite dimensional algebras.
On tolerant valuation rings.
On topological fields
On Torsion Points of Formal Groups over a Ring of Witt Vectors.
On Trace Forms of Algebraic Number Fields.
On trace forms of étale algebras and field extensions.
On trace forms of hilbertian fields.
On trinominals of type x...+Ax...+1.
On two types of complete discrete valuation fields
On valuations of nearfields
On valued function fields I.
On valued function fields II. Regular functions and elements with the uniqueness property.
On valued function fields III. Reductions of algebraic curves.
On varieties of Hilbert type
A variety over a field is of Hilbert type if is not thin. We prove that if is a dominant morphism of -varieties and both and all fibers , , are of Hilbert type, then so is . We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.
On Witt rings of function fields of real analytic surfaces and curves.
Let V be a paracompact connected real analytic manifold of dimension 1 or 2, i.e. a smooth curve or surface. We consider it as a subset of some complex analytic manifold VC of the same dimension. Moreover by a prime divisor of V we shall mean the irreducible germ along V of a codimension one subvariety of VC which is an invariant of the complex conjugation. This notion is independent of the choice of the complexification VC. In the one-dimensional case prime divisors are just points, in the two-dimensional...