The important subject of this learn monograph is the relation among p-adic modular types and p-adic Galois representations, and specifically the speculation of deformations of Galois representations lately brought by way of Mazur. The classical conception of modular kinds is believed recognized to the reader, however the p-adic concept is reviewed intimately, with plentiful intuitive and heuristic dialogue, in order that the ebook will function a handy aspect of access to investigate in that sector. the consequences at the U operator and on Galois representations are new, and should be of curiosity even to the specialists. an inventory of additional difficulties within the box is incorporated to steer the newbie in his study. The booklet will therefore be of curiosity to quantity theorists who desire to know about p-adic modular types, major them speedily to fascinating study, and likewise to the experts within the topic.

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