Abstract:

In this mini-course, we give an introduction to Hida’s construction of analytic families of ordinary p-adic modular forms and their associated Galois representations. We will explain Hida’s control theorems for ordinary p-adic modular forms and show how these theorems have been useful in relating certain Hecke algebras with universal Galois deformation rings. We will also explain examples and open problems on these topics.

Reference:

[1] Haruzo Hida, Iwasawa modules attached to congruences of cusp forms, Ann. Sci. Ec. Norm. Sup. 4^th series 19 (1986), 231-273;

[2] Haruzo Hida, Galois representations into $\mathrm{GL}_2(\mathbb{Z}_p[[X]])$ attached to ordinary cusp forms, Inventiones Math. 85 (1986), 545-613;

[3] Haruzo Hida, Elementary Theory of L-functions and Eisenstein series, LMSST 26, Cambridge University Press, Cambridge, 1993;

[4] Haruzo Hida, Geometric Modular Forms and Elliptic Curves, 2^nd edition, World Scientific Publishing Company, Singapore, 2011.

[5] Haruzo Hida, Hecke fields of analytic families of modular forms, J. Amer. Math. Soc. 24 (2011), 51-80.

Time:

9/22、9/29  ：  9:00-10:30，10:45-12:15