
Course unit
NUMBER THEORY 2
SC01120636, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
Mutuating
Course unit code 
Course unit name 
Teacher in charge 
Degree course code 
SC01120636 
NUMBER THEORY 2 
ADRIAN IOVITA 
SC1172 
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/02 
Algebra 
2.0 
Core courses 
MAT/03 
Geometry 
2.0 
Core courses 
MAT/05 
Mathematical Analysis 
2.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
2.0 
16 
34.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
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 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 padic 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. SwinnertonDyer, On ladic representations and congruences between the coefficients of modular forms. 
Textbooks (and optional supplementary readings) 

Sustainable Development Goals (SDGs)

