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- Arithmetic_and_geometric_Frobenius abstract "In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p, where p is a prime number. Namely, the mapping φ that takes r in R to rp is a ring endomorphism of R.The image of φ is then Rp, the subring of R consisting of p-th powers. In some important cases, for example finite fields, φ is surjective. Otherwise φ is an endomorphism but not a ring automorphism.The terminology of geometric Frobenius arises by applying the spectrum of a ring construction to φ. This gives a mappingφ*: Spec(Rp) → Spec(R)of affine schemes. Even in cases where Rp = R this is not the identity, unless R is the prime field. Mappings created by fibre product with φ*, i.e. base changes, tend in scheme theory to be called geometric Frobenius. The reason for a careful terminology is that the Frobenius automorphism in Galois groups, or defined by transport of structure, is often the inverse mapping of the 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.".
- Arithmetic_and_geometric_Frobenius wikiPageID "6988121".
- Arithmetic_and_geometric_Frobenius wikiPageRevisionID "459057897".
- Arithmetic_and_geometric_Frobenius hasPhotoCollection Arithmetic_and_geometric_Frobenius.
- Arithmetic_and_geometric_Frobenius subject Category:Algebraic_geometry.
- Arithmetic_and_geometric_Frobenius subject Category:Algebraic_number_theory.
- Arithmetic_and_geometric_Frobenius subject Category:Mathematical_terminology.
- Arithmetic_and_geometric_Frobenius comment "In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p, where p is a prime number. Namely, the mapping φ that takes r in R to rp is a ring endomorphism of R.The image of φ is then Rp, the subring of R consisting of p-th powers. In some important cases, for example finite fields, φ is surjective.".
- Arithmetic_and_geometric_Frobenius label "Arithmetic and geometric Frobenius".
- Arithmetic_and_geometric_Frobenius sameAs m.0g_2_m.
- Arithmetic_and_geometric_Frobenius sameAs Q4791119.
- Arithmetic_and_geometric_Frobenius sameAs Q4791119.
- Arithmetic_and_geometric_Frobenius wasDerivedFrom Arithmetic_and_geometric_Frobenius?oldid=459057897.
- Arithmetic_and_geometric_Frobenius isPrimaryTopicOf Arithmetic_and_geometric_Frobenius.