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  • Elliptic curves and periodes

    Minimizza tutto Espandi tutto

    Teacher: Prof. Cristiana Bertolin (cristiana.bertolin@unipd.it)

    Timetable:

    • 13/12/23  - 10:30 - 12:30 - Room 2BC30  (Torre Archimede)
    • 20/12/23  - 10:30 - 12:30 - Room 2BC30  (Torre Archimede)
    • 12/01/24  - 13:30 - 14:30 - Room 2AB40 (Torre Archimede) Prof. Waldschmidt


    Course requirements: Algebra, Calculus, Geometry, of the first level degree in mathematics .


     Aim    : To discover the geometrical origin of some transcendental conjectures.


    Examination and grading: Please contact the teacher of the course by e-mail


    Course contents    :
    •  Introduction to algebraic curves
    •  Elliptic curves over the field of complex numbers
    •   Geometrical description of the law group on elliptic curve
    •  The Weierstras ”p”-function, the Weierstrass ζ- function, and the Serre f_q-function with their doubly periodicity
    •  The differential forms of the first, the second and the third kind
    • The periods of an elliptic curves and their transcendence properties 

  • Books and pdf

    Books:

    • Silverman, J.H. The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics. Vol. 106. Springer-Verlag (1986). ISBN 0-387-96203-4. 
    • Silverman, J.H. An Introduction to the Theory of Elliptic Curves  (2006). Summer School on Computational Number Theory and Applications to Cryptography. University of Wyoming. 
    •  Waldschmidt, M. Algebraic independence of periods of elliptic functions. (2016). Winter School on modular functions in one and several variables, Goa University, December 2014. From notes by R. Thangadurai.
    • Christina Birkenhake, Herbert Lange, Complex Abelian Varieties, Grundlehren der mathematischen Wissenschaften (GL, volume 302)