In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p, where p is a prime number.
In some important cases, for example finite fields, φ is surjective.
The terminology of geometric Frobenius arises by applying the spectrum of a ring construction to φ.
Mappings created by fibre product with φ*, i.e. base changes, tend in scheme theory to be called geometric Frobenius.
As in the case of a cyclic group in which a generator is also the inverse of a generator, there are in many situations two possible definitions of Frobenius, and without a consistent convention some problem of a minus sign may appear.