IST Field and Algebraic Number Theory - Speakers and Syllabus

Field Theory

  • Week 1: Field Extensions, Automorphisms, Normal Extensions, Separable and Inseparable Extensions,The Fundamental Theorem of Galois Theory. (Chapter 1 of [1]).
  • Week 2: Necessary condition for solvability by radicals, Insolvability by radicals of the quintic, Finite Fields, Abelian and Cyclic Extensions, Sufficient condition for solvability by radicals. (Chapter 2 of [1]).

Algebraic Number Theory

  • Week 1: Elements integral over a ring, Integral Extensions, Integrally Closed Rings, Integers in quadratic number fields, Norms and Traces, The Discriminant, Cyclotomic Fields, Noetherian Rings and Modules,Dedekind domains, Norm of an Ideal. (Chapters 2 and 3 of [2]).
  • Week 2: Ideal Classes and the Unit Theorem, Finiteness of the ideal class group, Units in imaginary and real number rings, Splitting of Primes Ideals in an Extension Field, The Discriminant and Ramification, Splitiing of a prime number in a quadratic number field. (Chapters 4 and 5 of [2]).

Text Books:
[1] Patrick Morandi, Field and Galois Theory, Springer 1996.
[2] Pierre Samuel, Algebraic Theory of Numbers, Hermann Publishers, 1970.

Speakers and Course Associates
1. D. Surya Ramana, HRI Allahabad
2. Amit Kulshrestha, IISER Mohali
3. Dinesh Khurana, Panjab University, Chandigarh
4. Anjana Khurana, Panjab University, Chandigarh
5. Rahul Dattatraya Kitture, IISER Mohali

Time-Table
Tea Breaks: 11.00 - 11.30 and 3.30 - 4.00
Lunch Break: 1.00 - 2.30
Snacks: 5.00 - 5.30

  9.30 - 11.00
Lecture 1
11.30-1.00
Lecture 2
2.30-3.30
Tutorial 1
4.00-5.00
Tutorial 2
June 4 AK DK AK, AKh, RD AK, AKh, RD
June 5 AK DK DK, AKh, RD DK, AKh, RD
June 6 AK DK AK, AKh, RD AK, AKh, RD
June 7 AK DSR DSR, DK, RD DSR, DK, RD
June 8 AK DSR AK, AKh, RD AK, AKh, RD
June 9 AK DSR DSR, DK, RD DSR, DK, RD
June 11 AKh DSR AKh, DK, RD AKh, DK, RD
June 12 AKh DSR DSR, DK, RD DSR, DK, RD
June 13 AKh DSR AKh, DK, RD AKh, DK, RD
June 14 DK DSR DSR, DK, RD DSR, DK, RD
June 15 DK DSR DK, AKh, RD DK, AKh, RD
June 16 DK DSR DSR, DK, RD DSR, DK, RD