Study programme 2022-2023 | Français | ||
Seminars: Local Fields | |||
Programme component of Master's in Mathematics : Research Focus (MONS) (day schedule) à la Faculty of Science |
Code | Type | Head of UE | Department’s contact details | Teacher(s) |
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US-M2-MATHFA-006-M | Optional UE | VOLKOV Maja | S843 - Géométrie algébrique |
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Language of instruction | Language of assessment | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Credits | Weighting | Term |
---|---|---|---|---|---|---|---|---|---|
| Français | 30 | 0 | 90 | 0 | 0 | 12 | 12.00 | Full academic year |
AA Code | Teaching Activity (AA) | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Term | Weighting |
---|---|---|---|---|---|---|---|---|
S-MATH-034 | Seminars: Local Fields | 30 | 0 | 90 | 0 | 0 | A | 100.00% |
Programme component |
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Objectives of Programme's Learning Outcomes
Learning Outcomes of UE
Introduction to local fields.
The aim of this course is to master basic p-adic field theory .
UE Content: description and pedagogical relevance
Core: commutative algebra, inductive and projective limits, completions, absolute values and valuations, discrete valuation rings , p-adic fields, dévissages.
Further topics (non-exhaustive list):
- Algebraic number theory
- Galois cohomology
- Galois theory of p-adic extensions
- Hasse principle for rational quadratic forms
- Topics in p-adic analysis
- Witt vectors.
Prior Experience
Bachelor's degree Algebra and Analysis courses, basic commutative algebra.
Type of Teaching Activity/Activities
AA | Type of Teaching Activity/Activities |
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S-MATH-034 |
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Mode of delivery
AA | Mode of delivery |
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S-MATH-034 |
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Required Learning Resources/Tools
AA | Required Learning Resources/Tools |
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S-MATH-034 | M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley J.-P. Serre, Cours d'arithmétique, Presses Universitaires de France J. Neukirch, Algebraic Number Theory, Grundlehren der Mathematischen Wissenschaften 322 , Springer-Verlag |
Recommended Learning Resources/Tools
AA | Recommended Learning Resources/Tools |
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S-MATH-034 | Not applicable |
Other Recommended Reading
AA | Other Recommended Reading |
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S-MATH-034 | Not applicable |
Grade Deferrals of AAs from one year to the next
AA | Grade Deferrals of AAs from one year to the next |
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S-MATH-034 | Authorized |
Term 1 Assessment - type
AA | Type(s) and mode(s) of Q1 assessment |
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S-MATH-034 |
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Term 1 Assessment - comments
AA | Term 1 Assessment - comments |
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S-MATH-034 | Continuous assessment throughout the academic year. |
Resit Assessment - Term 1 (B1BA1) - type
AA | Type(s) and mode(s) of Q1 resit assessment (BAB1) |
---|---|
S-MATH-034 |
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Term 2 Assessment - type
AA | Type(s) and mode(s) of Q2 assessment |
---|---|
S-MATH-034 |
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Term 2 Assessment - comments
AA | Term 2 Assessment - comments |
---|---|
S-MATH-034 | Continuous assessment throughout the academic year. |
Term 3 Assessment - type
AA | Type(s) and mode(s) of Q3 assessment |
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S-MATH-034 |
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Term 3 Assessment - comments
AA | Term 3 Assessment - comments |
---|---|
S-MATH-034 | Not applicable |