Abstract: Given two Chow motives M and N satisfying Rost nilpotence, a natural question is whether their direct sum has the same property. Rather obviously this question is closely related to the famous and old Köthe conjecture. If this conjecture is true the answer to above question is yes. However it seems that most ring theorists believe Köthe's conjecture does not hold. This leads to studying stronger versions of Rost nilpotence, which (surprisingly?) hold in (almost?) all cases where usual Rost nilpotence is known, as I will explain in my talk.

Abstract: Given two Chow motives M and N satisfying Rost nilpotence, a natural question is whether their direct sum has the same property. Rather obviously this question is closely related to the famous and old Kothe conjecture. If this conjecture is true the answer to above question is yes. However it seems that most ring theorists believe Kothe's conjecture does not hold. This leads to studying stronger versions of Rost nilpotence, which (surprisingly?) hold in (almost?) all cases where usual Rost nilpotence is known, as I will explain in my talk.