In a seminal paper, Serre studied p-adic limits of modular forms with the aim of constructing
p-adic L-functions for totally real number fields. Since then, the theme of p-adic interpolation
of automorphic forms has played an important role in many achievements of contemporary
number theory, such as Wiles's proof of Fermat's Last Theorem. I will give a brief overview
of Serre's method and of the results of Hida, Coleman-Mazur, Buzzard and Chenevier in the
construction of p-adic families of modular forms and of their associated Galois representations.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/7671