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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.".
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- Arithmetic_and_geometric_Frobenius wikiPageOutDegree "25".
- Arithmetic_and_geometric_Frobenius wikiPageRevisionID "459057897".
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Affine_scheme.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Category:Algebraic_geometry.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Category:Algebraic_number_theory.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Category:Mathematical_terminology.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Characteristic_(algebra).
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Commutative_ring.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Cyclic_group.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Fibre_product.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Finite_field.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Frobenius_automorphism.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Frobenius_endomorphism.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Galois_group.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Grothendiecks_relative_point_of_view.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Inverse_function.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Inverse_mapping.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Mathematics.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Minus_sign.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Plus_and_minus_signs.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Prime_field.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Prime_number.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Pullback_(category_theory).
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Ring_endomorphism.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Ring_homomorphism.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Scheme_(mathematics).
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Scheme_theory.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Spectrum_of_a_ring.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Springer-Verlag.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Springer_Science+Business_Media.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Subring.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Surjective.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Surjective_function.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLink Transport_of_structure.
- Arithmetic_and_geometric_Frobenius wikiPageWikiLinkText "Arithmetic and geometric Frobenius".
- Arithmetic_and_geometric_Frobenius wikiPageWikiLinkText "arithmetic and geometric Frobenius".
- Arithmetic_and_geometric_Frobenius hasPhotoCollection Arithmetic_and_geometric_Frobenius.
- Arithmetic_and_geometric_Frobenius wikiPageUsesTemplate Template:Citation.
- 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 hypernym Number.
- 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.