{"product_id":"integration-of-one-forms-on-p-adic-analytic-spaces","title":"Integration of One-forms on P-adic Analytic Spaces","description":"Among 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. 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.\nIn 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. 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.","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":54221077905752,"sku":"9780691128627","price":80.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9780691128627_1ef3e7fe-031e-4bc5-b3c2-8a1d157f4da1.jpg?v=1771317012","url":"https:\/\/agendabookshop.com\/products\/integration-of-one-forms-on-p-adic-analytic-spaces","provider":"Agenda Bookshop","version":"1.0","type":"link"}