Date & Time: Wednesday, March 12, 2014, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: S. M. Bhatwadekar, Bhaskaracharya Pratishthana
Title: Projective modules over the kernel of a locally nilpotent derivation on an affine space
Abstract: Let $k$ be an algebraically closed field of characteristic zero, $D$ be a locally nilpotent derivation on the polynomial algebra $k[X_1, \cdots , X_n]$ and $A$ be the kernel of $D$. In this set up a question of Miyanishi asks whether finitely generated projective modules over $A$ are free. Note that for $n = 3$, by a result of Miyanishi, the kernel $A$ is a polynomial algebra in two variables over $k$ and hence an answer to the question is affirmative. In my talk I will address this question for $n = 4$.