Arithmetic of adjoint L-values
Student No.:50
Time:Mon/Wed 15:10-17:00, 12-8~12-31
Instructor:Haruzo Hida  [UCLA]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2014-12-8
Ending Date:2014-12-31


We discuss the following four topics:

1. Introduction to the ordinary (i.e. slope 0) Hecke algebras for elliptic modular forms;

2. Some basic ring theory to deal with Hecke algebras;

3.``$R=T$" theorem (of Wiles), and its relation to the adjoint Selmer groups;

4. Basics (analytic continuation, value at s=1, and so on) of adjoint L-function of elliptiuc modular forms;

5. Relation of adjoint L-values to congruence of modular forms and the adjoint Selmer groups (an example of the solution to a Iwasawa main conjecture).




Basic commutative ring theory [3], basics of modular form theory [1,Chapters 5-7], basics of Galois cohomology theory [2].




Hida's books

1. Elementary Theory of L-functions and Eisenstein series, LMSST 26, Cambridge University Press, Cambridge, 1993

2.Modular Forms and Galois Cohomology, Studies in Advanced Mathematics 69, Cambridge University Press, Cambridge, 2000

Commutative ring theory:

3. H. Matsumura, Commutative Ring Theory, Cambridge studies in advanced mathematics vol.8, Cambridge Univ. Press, 1986