Let X be a scheme such that# e Ox and let 1 be a line bundle over X. A quadratic space over
X with values in T is a triple (JF, h, 1), where F is a bundle over X and h is a selfdual …

We study degenerations of rank 3 quadratic forms and of rank 4 Azumaya algebras, and
extend what is known for good forms and Azumaya algebras. By considering line-bundle …

1.1. Functorial properties. After the appearance of Witt's paper it was a natural task to study
the functorial properties of the Witt ring and its relation to other functorial constructions like …

A (non-degenerate) quadratic form 4'over a field K of characteristic 4= 2 is called round if
either (i) it is a sum of hyperbolic forms or (ii) it is anisotropic and x~ b-~ 4'holds for all …

By a quadratic module over a commutative ring R, we mean a pair (M, q) with M a finitely
generated projective R-module and q: Mt R a quadratic form. We say that (M, q) is a …

Integral quadratic forms : applications to algebraic geometry Page 1 Astérisque IGOR
DOLGACHEV Integral quadratic forms : applications to algebraic geometry Astérisque, tome …

This book is a comprehensive study of the algebraic theory of quadratic forms, from classical
theory to recent developments, including results and proofs that have never been published …

Generalized Chow forms were introduced by Cayley for the case of 3-space; their zero set
on the Grassmannian G (1, 3) is either the set Z of lines touching a given space curve (the …

This paper is a sequel to [11] and [8] and in its main part relates the explicit computations of
quadratic forms given in [11] with the abstract classification in [8]. Let K be a field of …

As a special case he found that if f is unimodular we have (2) f (w, w)-r (mod 4), this was a
corollary of topological investigations of F. HIRZEBRUCH and H. HoPF [2]. Now it may be …