Integral quadratic forms : applications to algebraic geometry
Invariants of a quadratic form attached to a tame covering of schemes
We build on preceeding work of Serre, Esnault-Kahn-Viehweg and Kahn to establish a relation between invariants, in modulo 2 étale cohomology, attached to a tamely ramified covering of schemes with odd ramification indices. The first type of invariant is constructed using a natural quadratic form obtained from the covering. In the case of an extension of Dedekind domains, mains, this form is the square root of the inverse different equipped with the trace form. In the case of a covering of Riemann...
Isometries of quadratic spaces
Let be a global field of characteristic not 2, and let be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial if and only if such an isometry exists over all the completions of . This gives a partial answer to a question of Milnor.
Isotrope Unterräume rationaler quadratischer Formen.
Knebusch-Milnor exact sequence and parity of class numbers
Komposition und Klassenzahlen binärer quadratischer Formen
Le groupe des classes de l'algèbre affine d'une forme quadratique
Length spectra of the Hecke triangle groups.
Lineare Relationen zwischen Darstellungszahlen quadratischer Formen
Linearly Independent Zeros of Quadratic Forms over Number-Fields.
Local conditions for global representations of quadratic forms
Lower bounds for the principal genus of definite binary quadratic forms.
Markoff Forms and Primitive Words.
Matching Witts locally and globally
Modular lattices from finite projective planes
Using the geometry of the projective plane over the finite field , we construct a Hermitian Lorentzian lattice of dimension defined over a certain number ring that depends on . We show that infinitely many of these lattices are -modular, that is, , where is some prime in such that .The Lorentzian lattices sometimes lead to construction of interesting positive definite lattices. In particular, if is a rational prime such that is norm of some element in , then we find a dimensional...
O minimu forem kvadratických
On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings
Harbater, Hartmann and Krashen obtained in 2015 a criterion for the existence of rational points on projective (or principal) homogeneous varieties for rational connected algebraic groups defined over function fields of normal curves over a complete discrete valuation ring in terms of completions of local rings at special points. This was obtained by a reduction via Artin approximation to a related patching problem solved by the same authors in 2009. In the special case of projective quadrics, we...
On Even Unimodular Positive Definite Quadratic Lattices of Rank 32.
On indecomposable quadratic forms.
On indefinite binary quadratic forms and quadratic ideals.