Topics in arithmetic geometry

MATH-494 / 5 credits

Teacher:

Language: English

Remark: Pas donné en 2024-25

Summary

P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Zeta function.

Content

Construction and arithmetics of p-adics

Galois theory and the p-adic complex numbers

p-adic analysis

Zeta functions and rationality

p-adic manifolds and integration

 

Learning Prerequisites

Recommended courses

 

  • Rings and modules
  • Galois theory
  • Introduction to differentiable manifolds

 

Learning Outcomes

By the end of the course, the student must be able to:

  • Demonstrate an understanding of the construction and basic theory of p-adic numbers, as well as being able to do calculations involving them.

Teaching methods

course ex-cathedra and exercises

Resources

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Topics in arithmetic geometry
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Topics in arithmetic geometry
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Topics in arithmetic geometry
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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