School of Mathematics Colloquium

# A Cautionary Tale

## by Dr. Sourav Sen (TIFR, Mumbai)

Thursday, September 8, 2022 from to (Asia/Kolkata)
at AG-69
 Description Abstract: Let $A \subseteq B$ be integral domains and $G$ be a totally ordered Abelian group. D. Daigle has formulated certain hypotheses on degree function $\deg : B \rightarrow G \cup \lbrace - \infty \rbrace$ so that it is tame in characteristic zero, i.e., $\deg(D)$ is defined for all $A$-derivations $D: B \rightarrow B$. This study is important because each $D \in \der_k(B)$ for which $\deg(D)$ is defined, we can homogenize the derivation which is an important and useful tool in the study of $\G_a$-action on an algebraic variety. In arbitrary characteristic, $\G_a$-action on an affine scheme $\spec(B)$ can be interpreted in terms of exponential maps on $B$. In this talk we shall discuss analogous formulations of hypotheses on the degree function so that $\deg(\phi)$ is defined for each $A$-linear exponential map $\phi$ on $B$. This talk is based on a joint work with N. Gupta.