%0 Journal Article %T How to use finite fields for problems concerning infinite fields %A Jean-Pierre Serre %J Mathematics %D 2009 %I arXiv %X The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic. %U http://arxiv.org/abs/0903.0517v2