NCMW - Hida Theory and Iwasawa Main Conjecture over Q (2023)

Speakers and Syllabus

 Syllabus to be covered in terms of modules of 6 lectures each :

Name of the Speakers
with their affiliation.

No. of
Lectures

Detailed
Syllabus

Dipramit Majumdar,
IIT Madras

4 (6 Hours)

Algebraic Number Theory and Iwasawa Theory

Ribet’s converse to Herbrand’s theorem, Basic Iwasawa Theory, and basic properties of p-adic L-functions.

Bharathwaj Palvannan,
IISc Bangalore

4 (6 Hours)

Iwasawa Theory and Hida Theory

Ordinary Λ-adic modular forms, Hida theory and Λ-adic Galois representations.

Mahesh Kakde,
IISc Bangalore

4 (6 Hours)

Hida theory and Iwasawa Main Conjecture

Λ-adic modular forms and the Iwasawa Main Conjecture : proof over Q, proof over totally real fields F if time permits.

 

References:

  1. C. Skinner, Galois Representations, Iwasawa Theory, and Special Values of L-functions, CMI notes.
  2. S. Lang, Cyclotomic Fields I and II.
  3. L. Washington, Introduction to cylotomic fields.
  4. .K. Ribet. A modular construction of unramified p-extensions of Q(μp). Invent. Math.,34(3):151–162, 1976.
  5. H. Hida, Elementary Theory of L-functions and Eisenstein Series.
  6. H. Hida. Galois representations into GL2(Zp[X]]) attached to ordinary cusp forms. Invent. Math., 85:545–613, 1986.
  7. .A. Wiles. On ordinary λ-adic representations associated to modular forms. Inv. Math.,94(3):529–573, 1988
  8. B. Mazur and A. Wiles, Class fields of abelian extensions of Q. Invent. Math. 76 (2) :179–330, 1984.
  9. A. Wiles, The Iwasawa conjecture for totally real fields. Ann. of Math. (2) 131 (3):493–540, 1990.

 Names of the tutors with their affiliation :

  1. Pratiksha Shingavekar, IIT Madras.
  2. Anand Chitrao, TIFR Mumbai.
  3. Ravitheja Vangala, IISc Bangalore.

 

 

Time Table

Tentative time-table, mentioning names of the speakers and tutors with their affiliation:  

Day

Date

Lecture 1

9:30
–
11:00

Tea

11:00
–
11.30

Lecture 2

11:30
–
13:00

Lunch

13:00
-
14:30

Tutorial 1

14:30
-
15:30

Tutorial 2

16:00
-
17:00

Snacks

17:00
 

 

(name of the speaker)

 

(name of the
speaker)

 

 

 

 
Mon

04/12/23

DM

 

BP

 

DM+PS

BP+AC

 
Tues

05/12/23

DM

 

BP

 

DM+ PS

BP+AC

 
Wed

06/12/23

DM

 

BP

 

DM+PS

BP+AC

 
Thu

07/12/23

DM

 

MK

 

DM+PS

MK +RV

 
Fri

08/12/23

BP

 

MK

 

BP+AC

MK +RV

 
Sat

09/12/23

MK

 

MK

 

MK+RV

MK+RV

 

Speakers: Tutors:
DM: Dipramit Majumdar PS: Pratiksha Shingavekar
BP: Bharathwaj Palvannan AC: Anand Chitrao
MK: Mahesh Kakde RV: Ravitheja Vangala

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