Department of Mathematics
INDIAN INSTITUTE OF SCIENCE
Home
(current)
Research
Research Areas
All Publications
Faculty Publications (by author)
Research Landscape
Academic Review Reports
People
Chair & Committees
Faculty
NMI Distinguished Associates
Inspire Fellows/DST Young Scientists
Postdocs
Visitors
STUDENTS
Ph.D.
Integrated Ph.D.
Interdisciplinary Ph.D.
ALUMNI
Ph.D.
Undergraduate
Faculty
Inspire Faculty and DST scientists
Postdocs
Staff
Project Staff
Academics
COURSES
Current & Upcoming
Course Schedule
Academic Calendar
Final Examination Schedule
Catalogue
Mathematics Intranet
DEGREE PROGRAMMES
Ph.D. Programme
Integrated Ph.D. Programme
Undergraduate Programme
RESOURCES
Student Information Handbook
Scheme of Instruction
Undergrad Scheme of Instruction
Jobs
Faculty
Postdoctoral
News & Events
Seminars
News & Announcements
Events
Eigenfunctions Seminars
Thesis colloquium/defence
Bangalore Probability Seminar
Algebra & Combinatorics Seminar
Geometry & Topology Seminar
APRG Seminar
Student Seminars
Resources
IISc Mail
IISc Course Registration
IISc Intranet
MathSciNet
Computer/Network FAQs
Moodle
Changed E-mails (at IISc)
Mathematics Library
NBHM Regional Library
IFCAM
NMI
Chair & Committees
Contact Us
UTILITIES
Comprehensive Report Templates
TA form
Department Forms
IISc Forms
IISc SAP S/4 HANA
IAMS
Samadhan
Opportunities
MA 356: Class field theory: a course in arithmetic geometry
Credits: 3:0
Pre-requisites :
Basic algebra, commutative rings, Noetherian rings, basic number theory,
basic knowledge of Galois theory of fields.
Number fields and finite fields.
Syllabus:
Review of Dedekind domains and rings of integers in number fields.
Topology of discrete valuation fields.
Group cohomology and Galois cohomology.
Brauer group.
Brauer group of local fields.
Hasse principle for Brauer group.
Norm subgroups and their openness.
Class field theory for local and global fields.
Class field theory for compact curves over finite fields.
Class field theory for open curves over finite fields.
Suggested books and references:
J. P. Serre,
Local fields
, Graduate Texts in Mathematics. Vol. 67. Springer-Verlag. New York-Heidelberg. 1979.
J. Milne,
Lecture notes on class field theory
.
All Courses
Contact
:
+91 (80) 2293 2711, +91 (80) 2293 2265 ;
E-mail:
chair.math[at]iisc[dot]ac[dot]in
Last updated: 08 Dec 2021