As a complement to Joe Silverman's answer, you man make google scholar to alert you be e-mail of new published articles (and books, preprints, etc) which contains the word "p-adic" (or any key word you like). This is really helpful if you are interested in "what's new in the p-adic world".

As a complement to Joe Silverman's answer, you can make google scholar to alert you be e-mail of new published articles (and books, preprints, etc) which contain the word "p-adic" (or any key word you like). This is really helpful if you are interested in "what's new in the p-adic world".