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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
The Tate-Shafarevich group of an elliptic curve
 Zvěřina, Adam ; Šťovíček, Jan (advisor) ; Příhoda, Pavel (referee)
This thesis deals with the Tate-Shafarevich group and its relation to rational points on the curve and its rank. We first define the notion of profinite groups and characterize them as Galois groups of field extensions. Then we define the Tate-Shafarevich group using Galois cohomology and explain its relation to the rational points on the curve. Finally, we formulate the Birch-Swinnerton-Dyer conjecture, which relates the rank of an elliptic curve and the order of its Tate-Shafarevich group. 1
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Complex algebraic curves
 Zvěřina, Adam ; Šťovíček, Jan (advisor) ; Kazda, Alexandr (referee)
The thesis describes the relationship between algebraic curves and Riemann surfaces. We define Weierstrass ℘-function and prove some of its properties. We further prove that every complex algebraic curve can be regarded as a Riemann surface. Finally, we demonstrate that an elliptic curve can be parametrised with Weierstrass ℘-function. 1
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3 Zvěřina, Aleš
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