Deuteronomy 24 - This "indecency" cannot be adultery - the punishment for adultery is death. 2023

Deu 24:1
"When a man takes a wife and marries her, and it happens that she finds no favor in his eyes because he has found some indecency in her, and he writes her a certificate of divorce and puts it in her hand and sends her out from his house,

This law does not specifically institute divorce as a practice. Although it does mention that divorce is allowed for some "indecency." This "indecency" cannot be adultery because the punishment for adultery is death. The Hebrew word implies some form of nakedness:

6172. 'ervah, er-vaw'; from H6168; nudity, lit. (espec. the pudenda) or fig. (disgrace, blemish):--nakedness, shame, unclean (-ness).

This is apparently referring to some kind of indecency short of adultery. But it is not specified. The issue being addressed in this passage is not divorce itself. But it is addressing that of a divorced woman remarrying her husband after she had remarried previously.