Over a global field any finite number of central simple algebras exponent dividing m is split by common cyclic extension degree m. We show that the same property holds for function fields 2-dimensional excellent schemes over henselian local domain dimension one or two with algebraically closed residue field.

We extend an approach to Morse theory due to Harvey and Lawson to non compact manifolds. This provides a modified and arguably more natural version of Morse-Novikov theory, where the Novikov Ring is replaced by a new " Forward Laurent Ring ". A detailed development of standard Morse-Novikov theory is clarified in several ways. Geometrically: The Novikov complex is described as a subcomplex of t...

We show that there exists a real non-singular pseudoholomorphic sextic curve in the affine plane which is not isotopic to any real algebraic sextic curve. This result completes the isotopy classification of real algebraic affine M -curves of degree 6. Comparing this with the isotopy classification of real affine pseudoholomorphic sextic M -curves obtained earlier by the first author, we find th...

A quite basic fact about abelian varieties (and complex tori) is that the only line bundle in Pic 0 with non-trivial cohomology is the structure sheaf. Mumford, in his treatment of the dual abelian variety, made the far-reaching remark that this yields the following sheaf-theoretic formulation. Let A be an abelian variety (over an algebraically closed field) of dimension g, let us denote A = Pi...

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

We report on results about a study of algebraic graph invariants, based on computer exploration, and motivated by graph-isomorphism and reconstruction problems. c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Abridged English version Ulam’s reconstruction conjecture [3] asserts that a graph on n vertices, n > 3, is determined up to an isomorphism by the collectio...