| Abstract: | We study the essential dimension of exceptional connected simply connected algebraic groups over algebraically closed fields. In the present paper, we find upper estimates for the essential dimensions of the groupsF 4 ,E 6 , andE 7 . For the groupF 4 , the upper estimate, thus obtained coincides with the known lower estimate. We also prove the second Serre conjecture for the groupE 6 and for a function field. Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 539–547, October, 2000. |
