NUMBER THEORY 2

Second cycle degree in MATHEMATICS

Campus: PADOVA

Language: English

Teaching period: Second Semester

Lecturer: ADRIAN IOVITA

Number of ECTS credits allocated: 6


Syllabus
Prerequisites: Number Theory 1.
Examination methods: Homework exercices will be handed in weekly, there will be a midterm exam and written final.
Course unit contents: The course will develop the theory of local fields following J.-P. Serre's book: Local fields.
We will study: valuation rings, completions of valuation rings, complete discrete valuation fields of mixed charatcteristic and their fnite extensions, the ramification filtration of the the Galois group of a finite, Galois extesnion of a local field.
As an application we will study p-adic modular forms.i