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arXiv · 2312.01750

Rigidity and triangularity of an exponential map

P. M. S. Sai Krishna
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Abstract

Let $k$ be a field of arbitrary characteristic, $A$ be a domain and $K=\mathrm{frac}(A)$. Then (1) All exponential maps of $k^{[3]}$ are rigid, and we give a necessary and sufficient condition for the triangularity of $δ\in \mathrm{EXP}(k^{[3]})$. (2) If $δ\in \mathrm{EXP}(A^{[3]})$ such that $\mathrm{rank}(δ)=\mathrm{rank}(δ_K)$, then $δ$ is rigid and we give a necessary and sufficient condition for the triangularity of $δ$. When $k$ is of zero characteristic, $(1)$ is due to \cite{DD} and $(2)$ is due to \cite{KL}.

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P. M. S. Sai Krishna. 2024-12-17. Rigidity and triangularity of an exponential map. https://arxiv.org/abs/2312.01750

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