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

• Subject Area: Mathematics
• Term: from 2014 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 129719356

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.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 878: Groups, Geometry and Actions
• Applicant Institution: Universität Münster
• Project Heads: Professor Dr. Joachim Cuntz; Professor Dr. Christopher Deninger; Professor Dr. Thomas Nikolaus