Second Level Degree in Mathematics
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NUMBER THEORY 2 - 6 CFU
Teacher
Adrian Iovita
Scheduled Period
I Year - 2 Semester | 02/03/2020 - 12/06/2020
Hours: 48 (16 esercitazione, 32 lezione)
Prerequisites
Number Theory 1.
Target skills and knowledge
Some knowledge in commutative algebra and general topology.
Examination methods
Homework exercices will be handed in weekly, there will be a midterm exam and written final.
Assessment criteria
The homeworks will be worth 40% of the grade, the midterm exam 20% and the final 40%.
Course 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
Planned learning activities and teaching methods
Expositions on a blackboard.
Additional notes about suggested reading
J.-.P. Serre, Local fields.
H.P.F. Swinnerton-Dyer, On l-adic representations and congruences between the coefficients of modular forms.