Integration of One-Forms on P-adic Analytic Spaces pdf epub mobi txt 电子书下载 2026

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出版者:Princeton Univ Pr

作者:Berkovich, Vladimir G.

出品人:

页数:168

译者:

出版时间:2007-2

价格:$ 90.40

装帧:HRD

isbn号码:9780691127415

丛书系列:

图书标签:

p-adic analysis
p-adic geometry
integration
analytic spaces
one-forms
algebraic geometry
number theory
topology
functional analysis
differential forms

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具体描述

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. 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. 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.

该书旨在系统地探讨一个重要的数学主题，即将一阶形式进行研究与分析，并在特殊数论背景下，将其延伸到更为复杂的P-ád分析空间。这本书深入剖析了现代代数几何、解析几何以及函数分析的交汇点，揭示了不同领域之间紧密相连的理论脉络。作者在书中详细阐述了一系列基本概念，如一阶形式的定义与性质，以及其在构造更高维度空间中的应用。这些内容不仅帮助读者理解数学结构的深层逻辑，也为进一步研究提供了坚实的基础。书中特别强调了P-ád分析空间这一核心概念，通过严谨的推导和丰富的例子，展示了传统解析方法在这种特殊数域中的适用性与局限性。读者将能够了解如何在这些空间内定义一阶形式，并探索其在整数系数、模数约束及非标准分析框架下的表现。这种研究方向不仅拓展了经典分析理论的边界，也为现代代数数论与函数分析的发展提供了新的视角。内容安排上，书采用分章节结构，从基础定义逐步深入到具体应用和高级推广，每个部分都以清晰逻辑展开。作者通过丰富的例证、精确的数学公式和详尽的推导过程，使读者能够全面掌握这一复杂领域内的重要知识点。书中还特别注重理论与实际应用之间的桥梁，帮助读者更好地理解这些概念在当前研究中的重要性及其潜在价值。总体而言，这本书为广大学生和科研人员提供了一个全面、深入的学习路径。它不仅涵盖了基础理论，还强调创新思维与问题解决能力的培养，旨在激发对数学分析与几何结构的兴趣，并为后续研究奠定坚实的理论基础。这种详尽且系统化的内容设计，使其成为一本有深度和广泛应用价值的权威参考书。通过这部书，读者将能够更清晰地认识到数学分析中的核心思想，以及它们如何在不同领域间相互交织、共同推动理论进步。这种细致入微的内容安排，不仅有助于巩固已有知识，还能激发新的研究方向与思考空间。无论是初学者还是高级研究者，这本书都将是一份极具参考价值的重要资料。