The commuting derivations conjecture (Veronika Kikteva)
The talk of Veronika Kikteva at the Seminar of the Laboratory on Algebraic Transformation Groups.
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