Learn Turkish: Cinayet dosyalarını evde bırakmam. - I do not leave murder files at home.

This is the negative Aorist (simple present) tense for the first person ("I"). For most subjects, the negative Aorist uses -maz or -mez (like bırakmaz, "he/she does not leave"). However, "I" and "we" are irregular. Instead of keeping the -z, "I" drops it and uses -mam or -mem. So, bırak (leave) + -mam = bırakmam (I do not leave).

Why is it cinayet dosyaları instead of just cinayet dosyalar?

In Turkish, when you combine two nouns to make a new concept like "murder" (cinayet) and "files" (dosyalar), you have to link them using a compound marker on the second word. This marker looks exactly like the "his/her/its" possessive ending (-ı/i/u/ü). So, "murder files" becomes cinayet dosyaları.

Where does the -nı at the very end of dosyalarını come from?

Because the murder files are the specific direct object of the verb (you are not leaving the files), they need the accusative case ending (-ı). When adding case endings to a noun compound, Turkish requires the buffer letter -n- to bridge the compound marker and the case ending. That gives us dosyaları + n + ı = dosyalarını.

Does bırakmam mean I am not leaving them right now, or in general?

In general! The Aorist tense is used for habits, routines, and general truths. Saying bırakmam means "It is my rule/habit not to leave them." If you meant "I am not leaving them right now," you would use the present continuous tense: bırakmıyorum.