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Inertial law of quadratic forms on modules over plural algebra

Marek Jukl (1995)

Mathematica Bohemica

Quadratic forms on a free finite-dimensional module are investigated. It is shown that the inertial law can be suitably generalized provided the vector space is replaced by a free finite-dimensional module over a certain linear algebra over ( real plural algebra) introduced in [1].

Invariants of a quadratic form attached to a tame covering of schemes

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...

Isometries of quadratic spaces

Eva Bayer-Fluckiger (2015)

Journal of the European Mathematical Society

Let k be a global field of characteristic not 2, and let f k [ X ] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the completions of k . This gives a partial answer to a question of Milnor.

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