There are several synonyms for the phrase "keep in ignorance." One such synonym is "keep in the dark," which refers to purposely withholding information from someone. Another synonym is "conceal," which means to prevent something from being known or discovered. "Withhold" is another synonym, which means to hold back or keep something from someone. "Obscure" is also a synonym for "keep in ignorance," which means to make something unclear or difficult to understand. Lastly, "hide" is another synonym, which means to keep something secret or out of sight. Regardless of which synonym is used, they all convey the same message - intentionally keeping someone uninformed or unaware of something.