Integral quadratic forms : applications to algebraic geometry
Igor Dolgachev (1982/1983)
Séminaire Bourbaki
Philippe Cassou-Noguès, Boas Erez, Martin J. Taylor (2000)
Journal de théorie des nombres de Bordeaux
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...
Eva Bayer-Fluckiger (2015)
Journal of the European Mathematical Society
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.
H.P. Schlickewei, Wolfgang M. Schmidt (1989)
Mathematische Zeitschrift
Kazimierz Szymiczek (1996)
Acta Mathematica et Informatica Universitatis Ostraviensis
Horst Pfeuffer (1981)
Acta Arithmetica
Alain Bouvier (1978)
Publications du Département de mathématiques (Lyon)
Thomas A. Schmidt, Mark Sheingorn (1995)
Mathematische Zeitschrift
Martin Kneser (1967)
Mathematische Annalen
J.H.H. Chalk (1980)
Monatshefte für Mathematik
Rainer Schulze-Pillot (2009)
Acta Arithmetica
Hopkins, Kimberly, Stopple, Jeffrey (2010)
Integers
Harvey Cohn (1972)
Mathematische Annalen
Kazimierz Szymiczek (1991)
Mathematica Slovaca
Tathagata Basak (2014)
Journal de Théorie des Nombres de Bordeaux
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...
Karel Petr (1911)
Časopis pro pěstování mathematiky a fysiky
David Grimm (2016)
Banach Center Publications
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...
Michio Ozeki (1986)
Mathematische Zeitschrift
O.T.O. O'Meara (1980)
Journal für die reine und angewandte Mathematik
Tekcan, Ahmet (2008)
Novi Sad Journal of Mathematics