An introduction to $p$-adic and motivic zeta functions and the monodromy conjecture

Abstract

These notes give a basic introduction to the theory of $p$-adic and motivic zeta functions, motivic integration, and the monodromy conjecture.

Notes of a lecture at the French-Japanese Winter School on Zeta and L-functions (Miura, January 2008); to appear in the conference proceedings (Memoirs of the Mathematical Society of Japan)