## Prüfer group Let $F_p$ be the finite field with $p$-elements In the Prüfer $p$-group every element has precisely $p$ $p$-th roots. It is unique up to isomorphism. ## Tate module $End(Pr$ Prüfer $p$-group $p$-group [[Sylow's theorem|Sylow]] $p$-subgroup of $Q/Z$ consisting of those elements whose order is a power of $p$: $Z(p^\infty)=Z[1/p]/Z$ ## Frobenius automorphism (relative Frobenius lifts some problems with the plain frobenius of shemes) ##Frobenius element