- construction of p-adic numbers,
- p-adic integers, units,
- p-adic topology,
- Hensel's lemma,
- algebraic closure,
- Newton polygon,
- inertia and ramification groups
p-adic Numbers (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-40-24-M-4||p-adic Numbers||4.5 CP (135 h)|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg. SuSe|
|Level|| Bachelor (Specialization)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|P||42 h||93 h||
- About [MAT-40-24-K-4]: Title: "p-adic Numbers"; Presence-Time: 42 h; Self-Study: 93 h
- About [MAT-40-24-K-4]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 84141 ("p-adic Numbers")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.
- 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.