As a question of style, it is not fine to mix two languages. If you introduce a technical term, you are more than encouraged to put the English term in parenthesis, maybe with a quote:
Potenzreihen (Power Series [Cauchy87]) have the form ...
There is still Mathematics published in German, though less and less because authors actually want to be read, and there are still textbooks in German, which you can consult for the German expression for a mathematical concept. If you cannot find one, you get to translate yourself, trying to be as literal as possible. So adjunction space would become Adjunktionsraum, if (contrafactually) there would not be a German expression for it.
Ultimately of course, it is the guidelines of your university and / or of your advisor(s) that matter.