Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Abhyankars_conjecture> ?p ?o }
Showing triples 1 to 61 of
61
with 100 triples per page.
- Abhyankars_conjecture abstract "In abstract algebra, Abhyankar's conjecture is a 1957 conjecture of Shreeram Abhyankar, on the Galois groups of algebraic function fields of characteristic p. The soluble case was solved by Serre in 1990 and the full conjecture was proved in 1994 by work of Michel Raynaud and David Harbater.The problem involves a finite group G, a prime number p, and the function field of nonsingular integral algebraic curve C defined over an algebraically closed field K of characteristic p.The question addresses the existence of Galois extensions L of K(C), with G as Galois group, and with restricted ramification. From a geometric point of view L corresponds to another curve C′, and a morphismπ : C′ → C.Ramification geometrically, and by analogy with the case of Riemann surfaces, consists of a finite set S of points x on C, such that π restricted to the complement of S in C is an étale morphism. In Abhyankar's conjecture, S is fixed, and the question is what G can be. This is therefore a special type of inverse Galois problem.The subgroup p(G) is defined to be the subgroup generated by all the Sylow subgroups of G for the prime number p. This is a normal subgroup, and the parameter n is defined as the minimum number of generators ofG/p(G).Then for the case of C the projective line over K, the conjecture states that G can be realised as a Galois group of L, unramified outside S containing s + 1 points, if and only ifn ≤ s.This was proved by Raynaud.For the general case, proved by Harbater, let g be the genus of C. Then G can be realised if and only ifn ≤ s + 2 g.↑ ↑ ↑ ↑ ↑".
- Abhyankars_conjecture wikiPageExternalLink conjecture.html.
- Abhyankars_conjecture wikiPageID "3832555".
- Abhyankars_conjecture wikiPageLength "3795".
- Abhyankars_conjecture wikiPageOutDegree "30".
- Abhyankars_conjecture wikiPageRevisionID "657216254".
- Abhyankars_conjecture wikiPageWikiLink Abstract_algebra.
- Abhyankars_conjecture wikiPageWikiLink Algebraic_curve.
- Abhyankars_conjecture wikiPageWikiLink Algebraic_function_field.
- Abhyankars_conjecture wikiPageWikiLink Algebraically_closed.
- Abhyankars_conjecture wikiPageWikiLink Algebraically_closed_field.
- Abhyankars_conjecture wikiPageWikiLink Category:Algebraic_curves.
- Abhyankars_conjecture wikiPageWikiLink Category:Conjectures.
- Abhyankars_conjecture wikiPageWikiLink Category:Conjectures_which_were_proven.
- Abhyankars_conjecture wikiPageWikiLink Category:Galois_theory.
- Abhyankars_conjecture wikiPageWikiLink Category:Theorems_in_abstract_algebra.
- Abhyankars_conjecture wikiPageWikiLink Characteristic_(algebra).
- Abhyankars_conjecture wikiPageWikiLink Conjecture.
- Abhyankars_conjecture wikiPageWikiLink David_Harbater.
- Abhyankars_conjecture wikiPageWikiLink Field_(mathematics).
- Abhyankars_conjecture wikiPageWikiLink Finite_group.
- Abhyankars_conjecture wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Abhyankars_conjecture wikiPageWikiLink Galois_extension.
- Abhyankars_conjecture wikiPageWikiLink Galois_group.
- Abhyankars_conjecture wikiPageWikiLink Genus_(mathematics).
- Abhyankars_conjecture wikiPageWikiLink Inverse_Galois_problem.
- Abhyankars_conjecture wikiPageWikiLink Michel_Raynaud.
- Abhyankars_conjecture wikiPageWikiLink Morphism.
- Abhyankars_conjecture wikiPageWikiLink Normal_subgroup.
- Abhyankars_conjecture wikiPageWikiLink Prime_number.
- Abhyankars_conjecture wikiPageWikiLink Projective_line.
- Abhyankars_conjecture wikiPageWikiLink Purdue_University.
- Abhyankars_conjecture wikiPageWikiLink Ramification_(mathematics).
- Abhyankars_conjecture wikiPageWikiLink Riemann_surface.
- Abhyankars_conjecture wikiPageWikiLink Shreeram_Abhyankar.
- Abhyankars_conjecture wikiPageWikiLink Shreeram_Shankar_Abhyankar.
- Abhyankars_conjecture wikiPageWikiLink Sylow_subgroup.
- Abhyankars_conjecture wikiPageWikiLink Sylow_theorems.
- Abhyankars_conjecture wikiPageWikiLink Étale_morphism.
- Abhyankars_conjecture wikiPageWikiLinkText "Abhyankar's conjecture".
- Abhyankars_conjecture hasPhotoCollection Abhyankars_conjecture.
- Abhyankars_conjecture title "Abhyankar's conjecture".
- Abhyankars_conjecture urlname "AbhyankarsConjecture".
- Abhyankars_conjecture wikiPageUsesTemplate Template:Distinguish.
- Abhyankars_conjecture wikiPageUsesTemplate Template:MathWorld.
- Abhyankars_conjecture wikiPageUsesTemplate Template:Reflist.
- Abhyankars_conjecture subject Category:Algebraic_curves.
- Abhyankars_conjecture subject Category:Conjectures.
- Abhyankars_conjecture subject Category:Conjectures_which_were_proven.
- Abhyankars_conjecture subject Category:Galois_theory.
- Abhyankars_conjecture subject Category:Theorems_in_abstract_algebra.
- Abhyankars_conjecture hypernym Conjecture.
- Abhyankars_conjecture type Thing.
- Abhyankars_conjecture comment "In abstract algebra, Abhyankar's conjecture is a 1957 conjecture of Shreeram Abhyankar, on the Galois groups of algebraic function fields of characteristic p.".
- Abhyankars_conjecture label "Abhyankar's conjecture".
- Abhyankars_conjecture differentFrom Abhyankars_lemma.
- Abhyankars_conjecture sameAs m.0b2b29.
- Abhyankars_conjecture sameAs Q4667492.
- Abhyankars_conjecture sameAs Q4667492.
- Abhyankars_conjecture wasDerivedFrom Abhyankars_conjectureoldid=657216254.
- Abhyankars_conjecture isPrimaryTopicOf Abhyankars_conjecture.