AI 中文总结
本综述介绍启发p进霍奇理论的相关数学领域，呈现多位学者的核心成果，说明其所需的前置数学背景。
AI 中文摘要
本综述对启发p进霍奇理论的经典霍奇理论、算术几何与代数数论作入门评述，呈现Tate、Faltings和Scholze发展的该新领域基本成果及对应数学构造，要求具备代数几何与代数拓扑的部分背景知识。
英文摘要
This survey gives an introductory review of the classical Hodge theory, arithmetic geometry and algebraic number theory that inspires p-adic Hodge theory. Basic results in this new area developed by Tate, Faltings and Scholze are presented with corresponding mathematical constructions. Some background in algebraic geometry and algebraic topology is required
Comments50 pages
