The -adic local monodromy theorem for fake annuli
The p-adic differential equation y' = wy in the closed unit disk.
The period-index problem in WC-groups IV: a local transition theorem
Let be a complete discretely valued field with perfect residue field . Assuming upper bounds on the relation between period and index for WC-groups over , we deduce corresponding upper bounds on the relation between period and index for WC-groups over . Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of LLR models of torsors under abelian varieties with good reduction and...
The Picard-Vessiot closure in differential Galois theory
The prime spectrum of an infinite product of copies of Z
The Pythagoras number of some affine algebras and local algebras.
The Pythagorean closure of fields.
The quadratic form transfer and valuations.
The quasi-real extension of the real numbers
The radical factors of over finite fields.
The rationality of the Poincaré series associated to the p-adic points on a variety.
The reduced length of a polynomial with complex coefficients
The reduced Wittring
The regular inverse Galois problem over non-large fields
By a celebrated theorem of Harbater and Pop, the regular inverse Galois problem is solvable over any field containing a large field. Using this and the Mordell conjecture for function fields, we construct the first example of a field over which the regular inverse Galois problem can be shown to be solvable, but such that does not contain a large field. The paper is complemented by model-theoretic observations on the diophantine nature of the regular inverse Galois problem.
The Relative Separable Closure of a Valued Field in its Completion.
The representation of one quadratic form by another in valuated fields
The resultant of non-commutative polynomials
The roots of a polynomial depend continuously on its coefficients.
The Schur-Szegö composition of real polynomials of degree 2.