Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-40-24-K-4

p-adic Numbers (2V+1U, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
2 V Lecture 3.0 CP 28 h 62 h
1 U Exercise class (in small groups) 1.5 CP 14 h 31 h
(2V+1U) 4.5 CP 42 h 93 h

Basedata

SWS 2V+1U
CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg. SuSe
Level [4] Bachelor (Specialization)
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

Notice

In each summer semester at least one of the courses [MAT-40-24-K-4], [MAT-40-25-K-4] or [MAT-40-29-K-4] is offered.

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

  • construction of p-adic numbers,
  • p-adic integers, units,
  • p-adic topology,
  • Hensel's lemma,
  • algebraic closure,
  • Newton polygon,
  • inertia and ramification groups

Literature

  • F. Lorenz: Einführung in die Algebra II,
  • N. Koblitz: p-adic Numbers, p-adic Analysis, and Zeta-Functions,
  • I.B. Fenseko, S.V. Vostokov: Local Fields and their Extensions.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

Requirements for attendance (informal)

More advanced knowledge from the courses [MAT-12-22-K-3] and [MAT-12-21-K-3] is useful but not necessarily required.

Modules:

Courses

Requirements for attendance (formal)

None

References to Course [MAT-40-24-K-4]

Module Name Context
[MAT-40-24-M-4] p-adic Numbers P: Obligatory 2V+1U, 4.5 LP
Course-Pool Name
[MAT-40-2V-KPOOL-4] Elective Courses Algebra, Geometry and Computeralgebra (2V, B.Sc.)