Topic summary
Frobenius element
Extracted from the Wikipedia article Frobenius endomorphism.
Frobenius for global fields
In algebraic number theory, Frobenius elements are defined for extensions L/K of global fields that are finite Galois extensions for prime idealsΦ of L that are unramified in L/K. Since the extension is unramified the decomposition group of Φ is the Galois group of the extension of residue fields. The Frobenius element then can be defined for elements of the ring of integers of L as in the local case, by