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We report on a systematic study of optical properties of (Ga,Mn)As epilayers spanning the wide range of accessible Mn(Ga) dopings. The material synthesis was optimized for each nominal Mn doping in order to obtain films which are as close as possible to uniform uncompensated (Ga,Mn)As mixed crystals. We observe a broad maximum in the mid-infrared absorption spectra whose position exhibits a pre...
Education is by nature a process of change and growth. “Learning” implies movement from one status to another, “before knowing” “now knowing.” Longitudinal research, which involves the stud...
We improve Kolyvagin’s upper bound on the order of the p-primary part of the Shafarevich-Tate group of an elliptic curve of rank one over a quadratic imaginary field. In many cases, our bound is precisely the one predicted by the Birch and Swinnerton-Dyer conjectural formula.
Kolyvagin used Heegner points to associate a system of cohomology classes to an elliptic curve over Q and conjectured that the system contains a non-trivial class. His conjecture has profound implications on the structure of Selmer groups. We provide new computational and theoretical evidence for Kolyvagin’s conjecture. More precisely, we explicitly compute Heegner points over ring class fields...
This is an introduction to classical descent theory, in the context of abelian varieties over number fields.
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