Algebraic groups and motives of projective homogeneous varieties of outer type

• Applicants: Professor Dr. Nikita Geldhauser; Dr. Maksim Zhykhovich
• Subject Area: Mathematics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 432236229

The concept of motive is fundamental in modern algebraic geometry. Originally it was introduced by Alexander Grothendieck as an attempt to unify cohomology theories. Meanwhile motives became one of the main languages in algebraic geometry to formulate and to solve its problems. The subject of our investigations are algebraic groups over arbitrary fields with a focus on groups of outer type, homogeneous varieties, and their Chow motives. Our main goals include motivic decompositions of homogeneous varieties, discrete motivic invariants, study of algebraic cycles on homogeneous varieties and cohomological invariants of groups and torsors.

• DFG Programme: Research Grants