An introduction to p-adic L-functions — Lean blueprint

14. Iwasawa theory for modular forms🔗

The Kubota–Leopoldt picture of Parts I and II is the Iwasawa theory of \GL(1): Dirichlet characters are the algebraic automorphic forms for \GL(1), and \zeta_p is their p-adic L-function. The next case is \GL(2), whose automorphic forms are modular forms. Remarkably, all of the \GL(1) theory has a \GL(2) analogue for sufficiently nice modular forms, although the picture is not yet complete in full generality. This chapter records the three constructions and the comparison theorems that bind them.

  1. 14.1. Recapping the GL(1) picture
  2. 14.2. The GL(2) setting
  3. 14.3. The analytic p-adic L-function
  4. 14.4. The arithmetic p-adic L-function
  5. 14.5. The algebraic p-adic L-function and the Main Conjecture
  6. 14.6. Further generalisations