Study programme 2021-2022 | Français | ||
Seminars: Local Fields | |||
Programme component of Master's in Mathematics : Research Focus 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 .
Content of UE
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 Assessment for UE in Q1
Q1 UE Assessment Comments
Not applicable
Type of Assessment for UE in Q2
Q2 UE Assessment Comments
Not applicable
Type of Assessment for UE in Q3
Q3 UE Assessment Comments
Not applicable
Type of Resit Assessment for UE in Q1 (BAB1)
Q1 UE Resit Assessment Comments (BAB1)
Not applicable
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 Reading
AA | |
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S-MATH-034 |
Required Learning Resources/Tools
AA | Required Learning Resources/Tools |
---|---|
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 Reading
AA | |
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S-MATH-034 |
Recommended Learning Resources/Tools
AA | Recommended Learning Resources/Tools |
---|---|
S-MATH-034 | Not applicable |
Other Recommended Reading
AA | Other Recommended Reading |
---|---|
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 |
---|---|
S-MATH-034 | Authorized |