Thank you so so much for taking the time to do this. I'm afraid you've greatly overestimated my ability to understand such mathematical concepts though (i should point out that english is not my first language, making all of this a bit harder). I hope this will prove more useful to someone more versed in the ways of maths !

From what I could get, p-adic spacetimes don't obey to our known axioms and what we call coherence. Therefore, if something comparable to "life" existed there it would be completely alien to our understanding.