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Nov 16, 2023 at 6:34 comment added David Loeffler Unless you know more about your representation this question is unanswerable. It’s trivial to check that if T is a Zp-lattice in a crystalline representation, then you can always find T’ which is non-crystalline and congruent to T modulo an arbitrarily high power of p.
Nov 16, 2023 at 3:53 comment added tkr But in what format is the data of the $\rho_n$ handed to you? Like, what is the input of the calculation you anticipate wanting/needing?
Nov 16, 2023 at 2:41 comment added Richard @WillSawin You are right, but you could see my last para in the new edition.
Nov 16, 2023 at 2:39 history edited Richard CC BY-SA 4.0
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Nov 14, 2023 at 16:48 comment added David Loeffler I agree with the substance of Will’s comment - the question isn’t answerable until you tell us in what way the V in your problem is characterised. That said, a single element of Qp is in itself an “infinite amount of data”!
Nov 14, 2023 at 14:52 history edited YCor CC BY-SA 4.0
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Nov 14, 2023 at 14:03 history edited YCor CC BY-SA 4.0
formatting
Nov 14, 2023 at 13:45 comment added Will Sawin How is the representation $V$ described in your data? A Galois representation is a priori an infinite amount of data - what do you actually have that you want to calculate with?
Nov 14, 2023 at 13:35 history asked Richard CC BY-SA 4.0