$G_a$-actions and their applications

Abstract: Let $k$ be an algebraically closed field, $V$ be an affine $k$-variety and $A$ be its coordinate ring. A $G_a$-action on $V$ is an algebraic group action of the additive group $(k, +)$ on $V$. A $G_a$-action on $V$ gives rise to a certain ring homomorphism from $A$ to the polynomial ring $A[T]$ called an exponential map on the ring $A$. When $k$ is of characteristic zero, $G_a$-actions or exponential maps is conveniently studied through the concept of locally nilpotent derivations. Techniques from locally nilpotent derivations and exponential maps have provided crucial breakthroughs in solving some of the major challenging problems on polynomial rings. In this talk, we discuss a few examples of these developments.

Mathematics

Audience: learners

TMC Distinguished Lecture Series

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