nLab Iwasawa polynomial

Idea

As a construction in Iwasawa theory, the Iwasawa polynomial is a number theoretic analogue of the Alexander polynomial. (e.g. CL 12, plage 3)

The relation between the Alexander polynomial and the Lefschetz (spectral) zeta function is analogous to that between the Iwasawa polynomial and the p-adic analytic zeta function. See (Morishita 12, chapter 12).

A generator of the characteristic ideal of (the Pontryagin dual of the Selmer’s subgroup) $Sel(X_\inf ,\rho)^\ast$, called the twisted Iwasawa polynomial, is an analogue of the twisted Alexander polynomial.

References

• Chao Li, Iwasawa theory, lecture notes 2012 (pdf)

• Masanori Morishita, Knots and primes: an introduction to arithmetic topology, Springer 2012