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.
• 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.

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: topological groups and rings, 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 works

Q1 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q2

• Presentation and works

Q2 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

• Presentation and works

Q3 UE Assessment Comments

Not applicable

Q1 UE Resit Assessment Comments (BAB1)

Not applicable