Quaternions, polarizations and class numbers
نویسندگان
چکیده
منابع مشابه
Quaternions , polarizations and class numbers
We study abelian varieties A with multiplication by a totally indefinite quaternion algebra over a totally real number field and give a criterion for the existence of principal polarizations on them in pure arithmetic terms. Moreover, we give an expression for the number π 0 (A) of isomorphism classes of principal polarizations on A in terms of relative class numbers of CM fields by means of Ei...
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We present some elementary ideas to prove the following Sylvester-Gallai type theorems involving incidences between points and lines in the planes over the complex numbers and quaternions. (1) Let A and B be finite sets of at least two complex numbers each. Then there exists a line l in the complex affine plane such that |(A×B) ∩ l| = 2. (2) Let S be a finite noncollinear set of points in the c...
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A Sylvester-Gallai (SG) configuration is a finite set S of points such that the line through any two points in S contains a third point of S. According to the Sylvester-Gallai Theorem, an SG configuration in real projective space must be collinear. A problem of Serre (1966) asks whether an SG configuration in a complex projective space must be coplanar. This was proved by Kelly (1986) using a d...
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The goals of this paper are to provide: (I ) sufficient conditions, based on the solvability of certain diophantine equations, for the non-triviality of the dass numbers of certain real quadratic fields; (2) sufficient conditions for the divisibility of the class numbers of certain imaginary quadratic fields by a given integer; and (3) necessary and sufficient conditions for an algebraic intege...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2003
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crll.2003.065