Study programme 2021-2022Français
Seminars: Local Fields
Programme component of Master's in Mathematics : Research Focus à la Faculty of Science

CodeTypeHead of UE Department’s
contact details
Teacher(s)
US-M2-MATHFA-006-MOptional UEVOLKOV MajaS843 - Géométrie algébrique
  • VOLKOV Maja

Language
of instruction
Language
of assessment
HT(*) HTPE(*) HTPS(*) HR(*) HD(*) CreditsWeighting Term
  • Français
Français30090001212.00Full academic year

AA CodeTeaching Activity (AA) HT(*) HTPE(*) HTPS(*) HR(*) HD(*) Term Weighting
S-MATH-034Seminars: Local Fields3009000A100.00%

Programme component

Objectives of Programme's Learning Outcomes

  • Have integrated and elaborate mathematical knowledge.
    • Mobilise the Bachelor's course in mathematics to address complex issues and have profound mathematical expertise to complement the knowledge developed in the Bachelor's course.
    • Use prior knowledge to independently learn high-level mathematics.
    • Research mathematical literature in an efficient and relevant way.
    • Read research articles in at least one discipline of mathematics.
  • Carry out major projects.
    • Independently carry out a major project related to mathematics or mathematical applications. This entails taking into account the complexity of the project, its objectives and the resources available to carry it out.
    • Appropriately use bibliographic resources for the intended purpose.
    • Present the objectives and results of a project orally and in writing.
  • Communicate clearly.
    • make a structured and reasoned presentation of the content and principles underlying a piece of work, mobilised skills and the conclusions it leads to.
  • Adapt to different contexts.
    • Demonstrate thoroughness, independence, creativity, intellectual honesty, and ethical values.
  • Skill 6: Have acquired professional skills in relation to the objective defining the degree.
    • Have gained expertise and specialised knowledge in a field of mathematics in order to enter fully into the world of research.
    • Demonstrate intuition and creativity to tackle new mathematical problems.
    • Expose high-level mathematical results to a specialised audience.
  • Have integrated and elaborate mathematical knowledge.
    • Mobilise the Bachelor's course in mathematics to address complex issues and have profound mathematical expertise to complement the knowledge developed in the Bachelor's course.
    • Use prior knowledge to independently learn high-level mathematics.
    • Research mathematical literature in an efficient and relevant way.
  • Carry out major projects.
    • Independently carry out a major project related to mathematics or mathematical applications. This entails taking into account the complexity of the project, its objectives and the resources available to carry it out.
    • Appropriately use bibliographic resources for the intended purpose.
    • Present the objectives and results of a project orally and in writing.
  • Communicate clearly.
    • make a structured and reasoned presentation of the content and principles underlying a piece of work, mobilised skills and the conclusions it leads to.
  • Adapt to different contexts.
    • Demonstrate thoroughness, independence, creativity, intellectual honesty, and ethical values.

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

  • Presentation and/or works

Q1 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q2

  • Presentation and/or works

Q2 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

  • Presentation and/or works

Q3 UE Assessment Comments

Not applicable

Type of Resit Assessment for UE in Q1 (BAB1)

  • N/A

Q1 UE Resit Assessment Comments (BAB1)

Not applicable

Type of Teaching Activity/Activities

AAType of Teaching Activity/Activities
S-MATH-034
  • Préparations, travaux, recherches d'information

Mode of delivery

AAMode of delivery
S-MATH-034
  • Face to face

Required Reading

AA
S-MATH-034

Required Learning Resources/Tools

AARequired Learning Resources/Tools
S-MATH-034M.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
S-MATH-034

Recommended Learning Resources/Tools

AARecommended Learning Resources/Tools
S-MATH-034Not applicable

Other Recommended Reading

AAOther Recommended Reading
S-MATH-034Not applicable

Grade Deferrals of AAs from one year to the next

AAGrade Deferrals of AAs from one year to the next
S-MATH-034Authorized
(*) HT : Hours of theory - HTPE : Hours of in-class exercices - HTPS : hours of practical work - HD : HMiscellaneous time - HR : Hours of remedial classes. - Per. (Period), Y=Year, Q1=1st term et Q2=2nd term
Date de dernière mise à jour de la fiche ECTS par l'enseignant : 11/05/2021
Date de dernière génération automatique de la page : 06/05/2022
20, place du Parc, B7000 Mons - Belgique
Tél: +32 (0)65 373111
Courriel: info.mons@umons.ac.be