For a long time-at least from Fermat to Minkowski-the theory of quadratic forms was a part of
number theory. Much of the best work of the great number theorists of the eighteenth and …

The theory of finite-dimensional division algebras witnessed several breakthroughs in the
latter decades of the twentieth century. Important advances, such as Amitsur's construction of …

The aim of the Expositions is to present new and important developments in pure and
applied mathematics. Well established in the community over more than two decades, the …

One often tries to reduce problems about quadratic forms over a field F to the corresponding
problems over a related field whose structure is somewhat simpler. For example, a reduction …

Les algebres considerees dans cet article sont simples et de dimension tinie sur leur centre.
La dimension dun telle algbbre sur son centre est le carrt dun nombre entier appele degrh …

Untitled Page 1 Page 2 Bruno Kahn FORMES QUADRATIQUES SUR UN CORPS Page 3
Bruno Kahn Institut de Mathématiques de Jussieu, 175–179 rue du Chevaleret, 75013 Paris …

Let k be a perfect field with cohomological dimension [les] 2. Serre's conjecture II claims that
the Galois cohomology set H1 (k, G) is trivial for any simply connected semi-simple algebraic …

Let K be a field of characteristic different from 2. In the algebraic theory of quadratic forms,
one studies the Witt ring W (K) of equivalence classes of non-degenerate quadratic forms …

Soit F un corps commutatif de caractéristique# 2. Le u-invariant de F est le plus petit entier
tel que toute forme quadratique sur F de rang &# x3E; soit isotrope, ou-f-oo si un tel entier …

Let F be any field, let D be a central simple F-algebra, and let X= SB (D) corresponding
Severi-Brauer variety [1]. The computation of certain K-cohomology groups of X played the …