What is the linguistic term for re-writing a written text from non-standard dialect to standard dialect of the same language?
Translation is the conversion of text from one language to another.
Since we keep the same language, and just change the dialect, I would rule out translation.
Transliteration is a type of conversion of a text from one script to another that involves swapping letters (thus trans- + liter-) in predictable ways (such as α → a, д → d, χ → ch, ն → n or æ → e).
We stay in the same script and don't swap letters, so this doesn't seem to fit either.
Is there a separate term at all, or do linguistics use a broader definition for translation in such a case?