Fundamental groups in Algebraic Geometry
主 题: Fundamental groups in Algebraic Geometry
报告人: Professor Helene Esnault (Berlin Free University)
时 间: 2013-10-18 14:00-15:00
地 点: 理科一号楼1114 (Room 1114 in the building of Math School) （数学所活动）
Topological fundamental groups of topological manifolds were defined in the 19th century. Applied to Riemann surfaces, they describe their uniformization. Riemann existence theorem implies that its profinite completion has a meaning in Algebraic Geometry over other fields. It leads to Grothendieck's theory of the \'etale fundamental group in Arithmetic Geometry, which encompasses Galois theory as well. In complex algebraic geometry, the Riemann-Hilbert correspondence describes purely algebraically the proalgebraic completion of the topological fundamental group. A theorem of Malcev-Grothendieck asserts that the \'etale fundamental group controls it. We describe analogues in characteristic $p>0$ of the concept of proalgebraic completion, and of the theorem of Malcev-Grothendieck.