In English one normally capitalizes both nouns and adjectives that refer to languages, peoples, religions, geographic regions etc., Thus "A Catholic priest spoke in French about his Antarctic exploration at a German university." Writing "abelian" with a lower-case initial "a" while "Euclidean" has a capital "E" is inconsistent usage and can be justified only by the fact that it's conventional. Sometimes one sees "euclidean" with a lower-case initial "e", but making some of these conventionally lower case while others are conventionally capital would lead to needless complication. I am philosophically opposed to needless complications.
German follows a different rule: all nouns have a capital initial letter; all adjectives have a lower-case initial except when capitalized for some other reason such as being at the beginning of a sentence or in signs in which all letters are capital. Thus:
"Die euklidische Geometrie" (de.wikipedia.org/wiki/Euklidische_Geometrie).
"Eine riemannsche Fläche" (de.wikipedia.org/wiki/Riemannsche_Fläche).