Equivariant and weak orientations in the motivic homotopy theory

• Applicants: Dr. Alexey Ananyevskiy, Ph.D.; Professor Dr. Nikita Geldhauser
• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 533047891

The present project belongs to the field of motivic homotopy theory (also known as A1-homotopy theory), an area of mathematics that brings powerful methods of the modern homotopy theory to study problems arising in the field of algebraic geometry, and also provides new perspectives on the classical homotopy theory from the algebraic point of view. The overall objective for this project is to develop a theory of orientations in the setting of the equivariant motivic homotopy theory and to study weak orientations, such as SL-orientation, in the motivic setting. We plan to investigate an equivariant motivic version of Riemann-Roch type theorems, an equivariant motivic Conner-Floyd theorem, SL-oriented cohomology theories and Riemann-Roch type theorems for them, and related problems.

• DFG Programme: Research Grants