MR1794067 (2001i:14032) Besser, Amnon(D-MUNS-GFM) A generalization of Coleman’s -adic integration theory. (English summary) Invent. Math. 142 (2000), no. 2, 397–434. Check this MR review, and add links to the various things mentioned there, syntomic etc. This article seems to be a possible starting point for exploring the “p-adic world”. Make sure to add all the references in this MR to the database.
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