### Grothendieck-Serre's conjecture for adjoint groups of types E_6 and E_7 , by Ivan Panin , Victor Petrov , and Anastasia Stavrova

In this preprint we prove cetain interesting results concerning principal
G-bundles, where G is an adjoint reductive group schemesof types E_6 and E_7.
Specifically, assume that R is a semi-local regular ring containing an infinite
perfect field, or that R is a semi-local ring of several points on a smooth
scheme over an infinite field. Let K be the field of fractions of R. Let H be
a strongly inner adjoint simple algebraic group of type E_6 or E_7 over R. We
prove that under the above assumptions every principal H-bundle P which has a
K-rational point is itself trivial. This confirms a conjecture posed by Serre
and Grothendieck.

Ivan Panin <panin at pdmi.ras.ru >

Victor Petrov <victorapetrov at googlemail.com >

Anastasia Stavrova <a_stavrova at mail.ru >