First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
NUMBER THEORY 2
SC01120636, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18
N0
bring this page
with you
Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination NUMBER THEORY 2
Website of the academic structure http://matematica.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA

Lecturers
Teacher in charge ADRIAN IOVITA MAT/03

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
SC01120636 NUMBER THEORY 2 ADRIAN IOVITA SC1172

ECTS: details
Type Scientific-Disciplinary 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

Mode of delivery (when and how)
Period Second semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 2.0 16 34.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 26/02/2018
End of activities 01/06/2018

Syllabus
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 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.
Textbooks (and optional supplementary readings)