{"product_id":"integration-of-one-forms-on-p-adic-vladimir-g-berkovich-9780691128627","title":"Integration of One-Forms on P-Adic Analytic Spaces","description":"\u003cp\u003eAmong the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path. \u003cp\u003e\u003c\/p\u003e Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Vladimir G. Berkovich\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691128626\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691128627\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/03\/2006\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 168\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.59lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.22h x 6.38w x 0.49d","brand":"Vladimir G. Berkovich","offers":[{"title":"Paperback","offer_id":48086766485759,"sku":"9780691128627","price":81.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_6946c06d-eb43-4172-9b13-a99a4bc328b9.jpg?v=1769096452","url":"https:\/\/www.whiterainbookhouse.com\/products\/integration-of-one-forms-on-p-adic-vladimir-g-berkovich-9780691128627","provider":"WR Book House","version":"1.0","type":"link"}