Random Galois extensions of Hilbertian fields
Let be a Galois extension of a countable Hilbertian field . Although need not be Hilbertian, we prove that an abundance of large Galois subextensions of are.
Rational Puiseux expansions
Reducibility of a special symmetric form
Irreducibility over of a special symmetric form in a variables is proved for .
Reducibility of lacunary polynomials II
Reducibility of lacunary polynomials. X
Reducibility of lacunary polynomials, XI
Reducibility of lacunary polynomials XII
Reducibility of quadrinomials
Reducibility of Symmetric Polynomials
A necessary and sufficient condition is given for reducibility of a symmetric polynomial whose number of variables is large in comparison to degree.
Reduction and specialization of polynomials
We show explicit forms of the Bertini-Noether reduction theorem and of the Hilbert irreducibility theorem. Our approach recasts in a polynomial context the geometric Grothendieck good reduction criterion and the congruence approach to HIT for covers of the line. A notion of “bad primes” of a polynomial P ∈ ℚ[T,Y] irreducible over ℚ̅ is introduced, which plays a central and unifying role. For such a polynomial P, we deduce a new bound for the least integer t₀ ≥ 0 such that P(t₀,Y) is irreducible...
Remarks and corrections to the paper "Principal ideal theorems for holomorphy rings in fields".
Remarks on existentially closed fields and diophantine equations
Remarks on the Algebraic Approach to Intersection Theory.
Representation theory of local division algebras.
Représentations comme sommes de carrés
Representations of multivariate polynomials by sums of univariate polynomials in linear forms
The paper is concentrated on two issues: presentation of a multivariate polynomial over a field K, not necessarily algebraically closed, as a sum of univariate polynomials in linear forms defined over K, and presentation of a form, in particular a zero form, as the sum of powers of linear forms projectively distinct defined over an algebraically closed field. An upper bound on the number of summands in presentations of all (not only generic) polynomials and forms of a given number of variables and...
Řešení algebraické rovnice výrazy meznými
Ritt's Second Theorem in arbitrary characteristic.
Root continuity theorems in valued fields.
Root continuity theorems in valued fields. II.