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    Brauer groups of 1-motives

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    Over a normal base scheme, we prove the generalized Theorem of the Cube for 1-motives and that a torsion class of the group He ́t2(M,Gm,M) of a 1-motive M, whose pull-back via the unit section ε:S→M is zero, comes from an Azumaya algebra. In particular, we deduce that over an algebraically closed field of characteristic zero, all classes of He ́t2(M,Gm,M) come from Azumaya algebras

    A note on divisorial Correspondences of extensions of abelian schemes by tori

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    Let S be a locally noetherian scheme and consider two extensions G1 and G2 of abelian S-schemes by S-tori. In this note we prove that the fppf-sheaf (Formula presented.) of divisorial correspondences between G1 and G2 is representable. Moreover, using divisorial correspondences, we show that line bundles on an extension G of an abelian scheme by a torus define group homomorphisms between G and (Formula presented.) Dedicated to M. Raynaud

    Voltage tunable SiGe photodetector: A novel tool for crypted optical communications through wavelength mixing

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    A novel tandem SiGe-Si device is demonstrated which, based on different photoresponses in two back-to-back diodes, exhibits a voltage tunable spectral responsivity. This feature, in conjunction with a wavelength dependence in the current direction, allows the efficient decryption of a signal when substantial noise is added to distinct carrier frequencies. Time dependent encryption schemes are also possible via a modulated voltage bias. (C) 1997 American Institute of Physics
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