The commuting derivations conjecture (Вероника Киктева)
Доклад Вероники Киктевой на семинаре лаборатории алгебраических групп преобразований.
In this talk we shall consider the Commuting Derivations Conjecture in dimension three: if D_1 and D_2 ∈ LND, which are linearly independent and satisfy [D_1; D_2] = 0, then ker D_1 ∩ ker D_2 = C[f], where f is a coordinate. Then it is shown that if the Commuting Derivations Conjecture in dimension n, the Cancellation Problem and Abhyankar–Sataye Conjecture in dimension n−1, all have an affirmative answer, then we can describe all coordinates of the form p(X)Y + q(X; Z_1; ... ; Z_n−1). Also, conjectures about possible generalisations of the concept of “coordinate” for elements of general rings are made.This talk will be based on the paper of Stefan Maubach [1].
References:
[1] Stefan Maubach, The commuting derivations conjecture, Journal of Pure and Applied Algebra 179 (2003) 159 – 168