Generalized cohomology theories and applications to algebraic and arithmetic geometry (A07)

广义上同调理论及其在代数和算术几何中的应用（A07）

• 批准号: 260662670
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/260662670?language=en
• 关键词: Generalized; cohomology; theories; applications; algebraic

Cohomology theories pervade large parts of algebraic and arithmetic geometry. In this project we will develop and study cohomology theories, especially in mixed characteristic that generalize and unify étale cohomology, crystalline cohomology and de Rham cohomology resp. Hochschild homology in the non-commutative setting. A main goal is to construct a cohomology theory that can serve the same purposes for arithmetic schemes as the l-adic or crystalline cohomology with their Frobenius actions for varieties over finite fields. Ideas from algebraic geometry, algebraic topology, operator algebras and analysis blend in these investigations.

统一理论遍布代数和算术几何形状的大部分。在这个项目中，我们将开发和研究共同体学理论，尤其是在概括和统一étale的共同体，晶体同谋和DE RHAM共同体学的混合特征中。在非共同环境中的Hochschild同源性。一个主要目标是构建一种共同体学理论，该理论可以为算术方案提供与L-ADIC或晶体共同体相同的目的，并及其Frobenius的作用用于有限领域的变化。这些调查中来自代数几何，代数拓扑，代数代数和分析的思想。