Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-40-27-K-6

Elliptic Curves in Positive Characteristics (2V, 3.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 3.0 CP 28 h 62 h
(2V) 3.0 CP 28 h 62 h

Basedata

SWS 2V
CP, Effort 3.0 CP = 90 h
Position of the semester 1 Sem. irreg.
Level [6] Master (General)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State [NORM] Active

Contents

  • plane projective cubics over arbitrary fields, rational points,
  • endomorphisms of elliptic curves, isogenies, complex multiplication, moduli,
  • counting of rational points, Hasse bound, Weil conjectures, Schoof's algorithm,
  • constructions of elliptic curves, quadratic twist, good/bad reduction,
  • special algorithms, discrete logarithm for elliptic curves, factorisation.

Literature

  • J .Silverman, The Arithmetic of Elliptic Curves.

Materials

Further literature will be announced in the lecture.

Requirements for attendance (informal)

More advanced knowledge of Algebra (e.g. from the courses [MAT-12-21-K-3] or [MAT-12-22-K-3]) are useful but not necessarily required.

Modules:

Courses

Requirements for attendance (formal)

None

References to Course [MAT-40-27-K-6]

Module Name Context
[MAT-40-27-M-6] Elliptic Curves in Positive Characteristics P: Obligatory 2V, 3.0 LP
Course-Pool Name
[MAT-40-2V-KPOOL-4] Elective Courses Algebra, Geometry and Computeralgebra (2V, B.Sc.)