anabelian

A1N1A1B3E1L1I1A1N1
/ˌænəˈbiliən/

adjective

Of or relating to anabelian geometry, a proposed theory describing the way the algebraic fundamental group G of an algebraic variety (or some related geometric object) V determines how V can be mapped into another geometric object W, under the assumption that G is very far from being an abelian group, in a sense to be made more precise.

Scrabble 11
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Meanings

adjectiveanabelian (not comparable)
  1. not comparablealgebraic geometryOf or relating to anabelian geometry, a proposed theory describing the way the algebraic fundamental group G of an algebraic variety (or some related geometric object) V determines how V can be mapped into another geometric object W, under the assumption that G is very far from being an abelian group, in a sense to be made more precise.

    We will formulate Grothendieck's anabelian conjectures in a more general context later, after having presented the basic facts about ́etale fundamental groups.

    2012, Florian Pop, “Lectures on anabelian phenomena in geometry and arithmetic”, in John Coates, Minhyong Kim, Florian Pop, Mohamed Saïdi, Peter Schneider, editors, Non-abelian Fundamental Groups and Iwasawa Theory, Cambridge University Press, page 5
    2 more examples

    We end up this section with the following remarks, both for the sake of completeness, but mostly because of the relevance of the facts we want to mention for the anabelian phenomena.

    2000, Florian Pop, “Alterations and Birational Anabelian Geometry”, in H. Hauser, J. Lipman, F. Oort, A. Quirós, editors, Resolution of Singularities, Birkhäuser, page 522

    But the interplay between those two parts remains mysterious and is at the source of some of the most standard conjectures about fundamental groups such as anabelian conjectures or the section conjecture.

    2013, Anna Cadoret, “Galois Categories”, in Pierre Dèbes, Michel Emsalem, Matthieu Romagny, A. Muhammed Uludağ, editors, Arithmetic and Geometry Around Galois Theory, Springer (Birkhäuser), page 172

Origin

From an- (“not”) + abelian (“commutative”); coined to imply a nuancedly stronger condition than "merely" noncommutative (see an-).

Full word history & related roots →

Rhymes & wordplay

Rhymes with anabelian

abelianperihelionaphelionanthelionmycelianOphelianparanthelionparhelion
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Cite this entry
APA

anabelian. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/anabelian

MLA

“anabelian.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/anabelian. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “anabelian,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/anabelian.

Source: anabelian on Wiktionary, CC BY-SA 4.0.