Elliptic Curves

Some articles on elliptic curves, elliptic, elliptic curve, curve:

Wiles's Proof Of Fermat's Last Theorem - Announcement and Subsequent Developments - Announcement and Final Proof (1993 - 1995)
... proof of the Taniyama–Shimura conjecture for semi-stable elliptic curves, and hence of Fermat's Last Theorem, over the course of three lectures delivered at the Isaac Newton ... and on 24 October 1994, Wiles submitted two manuscripts, "Modular elliptic curves and Fermat's Last Theorem" and "Ring theoretic properties of certain Hecke algebras", the ... These papers established the modularity theorem for semistable elliptic curves, the last step in proving Fermat's Last Theorem, 358 years after it was conjectured ...
Elliptic Cohomology - Definitions and Constructions
... A particularly rich source for formal group laws are elliptic curves ... A cohomology theory A with is called elliptic if it is even periodic and its formal group law is isomorphic to a formal group law of an elliptic curve E over R ... The usual construction of such elliptic cohomology theories uses the Landweber exact functor theorem ...
Enriques–Kodaira Classification - Surfaces of Kodaira Dimension 0 - Abelian Surfaces and 2-dimensional Complex Tori
... One dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic ... Criteria to be a product of two elliptic curves (up to isogeny) were a popular study in the nineteenth century ... Hodge diamond 1 ... Examples A product of two elliptic curves ...
Counting Points On Elliptic Curves - Bibliography
... Smart Elliptic Curves in Cryptography, Cambridge University Press, 1999 ... Enge Elliptic Curves and their Applications to Cryptography An Introduction ... Schoof Counting Points on Elliptic Curves over Finite Fields ...
Counting Points On Elliptic Curves
... An important aspect in the study of elliptic curves is devising effective ways of counting points on the curve ... and Digital Signature Authentication (See elliptic curve cryptography and elliptic curve DSA) ... effective use of the difficulty of the discrete logarithm problem (DLP) for the group, of elliptic curves over a finite field, where q = pk and p is a prime ...

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