Two-dimensional complex tori with multiplication by
$\sqrt {d}$ |
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Authors: | Wolfgang M Ruppert |
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Institution: | Mathematisches Institut, Universit?t Erlangen-Nürnberg, Bismarckstra?e 1 1/2, D-91054 Erlangen, Germany, DE
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Abstract: | We give an elementary argument for the well known fact that the endomorphism algebra
End(A)?\Bbb Q {\rm {End}}(A)\otimes {\Bbb Q } of a simple complex abelian surface A can neither be an imaginary quadratic field nor a definite quaternion algebra. Another consequence of our argument is that a two-dimensional complex torus T with
\Bbb Q (?d)\hookrightarrow End\Bbb Q (T){\Bbb Q }(\sqrt {d})\hookrightarrow {\rm{End_{{\Bbb Q }}}}(T) where
\Bbb Q (?d){\Bbb Q }(\sqrt {d}) is real quadratic, is algebraic. |
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Keywords: | |
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