Discriminant of Symplectic Involutions
نویسندگان
چکیده
منابع مشابه
Discriminant of Symplectic Involutions
We define an invariant of torsors under adjoint linear algebraic groups of type Cn—equivalently, central simple algebras of degree 2n with symplectic involution—for n divisible by 4 that takes values in H(k, μ2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple alg...
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Let V be a 2n-dimensional vector space over a field F and Ω be a non-degenerate symplectic form on V . Denote by Hk(Ω) the set of all 2k-dimensional subspaces U ⊂ V such that the restriction Ω|U is non-degenerate. Our main result (Theorem 1) says that if n 6= 2k and max(k, n−k) ≥ 5 then any bijective transformation of Hk(Ω) preserving the class of base subsets is induced by a semi-symplectic au...
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An invariant for symplectic involutions on central simple algebras of degree divisible by 4 over fields of characteristic different from 2 is defined on the basis of Rost’s cohomological invariant of degree 3 for torsors under symplectic groups. We relate this invariant to trace forms and show how its triviality yields a decomposability criterion for algebras with symplectic involution.
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A formula is given for the discriminant of the tensor product of the canonical involution on a quaternion algebra and an orthogonal involution on a central simple algebra of degree divisible by 4. As an application, an alternative proof of Shapiro’s “Pfister Factor Conjecture” is given for tensor products of at most five quaternion algebras. Throughout this paper, the characteristic of the base...
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Classification of real K3 surfaces X with a non-symplectic involution τ is considered. For some exactly defined and one of the weakest possible type of degeneration (giving the very reach discriminant), we show that the connected component of their moduli is defined by the isomorphism class of the action of τ and the anti-holomorphic involution φ in the homology lattice. (There are very few sim...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2009
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2009.v5.n1.a11