The critical subject of this learn monograph is the relation among p-adic modular varieties and p-adic Galois representations, and particularly the idea of deformations of Galois representations lately brought through Mazur. The classical idea of modular kinds is thought recognized to the reader, however the p-adic idea is reviewed intimately, with abundant intuitive and heuristic dialogue, in order that the booklet will function a handy aspect of access to analyze in that region. the consequences at the U operator and on Galois representations are new, and may be of curiosity even to the specialists. an inventory of additional difficulties within the box is incorporated to lead the newbie in his learn. The ebook will hence be of curiosity to quantity theorists who desire to know about p-adic modular kinds, top them speedily to fascinating examine, and likewise to the experts within the topic.

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