A^1-homotopy sheaves - new perspectives

• Applicant: Anand Sawant, Ph.D.
• Subject Area: Mathematics
• Term: from 2017 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 355068532

• Final Report Year: 2019

Final Report Abstract

The A1-fundamental group of a split reductive group was computed. This computation was achieved by developing a cellular version of A1-homology and computing it in low degrees for split, semisimple, simply connected algebraic groups and their flag varieties. Using purely algebro-geometric methods, the sheaf of A1-connected components of a smooth projective surface, which is birationally ruled over a curve of genus > 0. As a consequence, Morel’s conjecture about the A1-invariance of the sheaf of A1-connected components was shown to hold for all smooth projective surfaces over an algebraically closed field of characteristic 0.

Publications

• A1-connected components of ruled surfaces
  Chetan Balwe, Anand Sawant