arXiv subjects

P. M. S. Sai Krishna

Publications and source records attributed to P. M. S. Sai Krishna.

2 recordsLinked to original sources

arXiv2024

Rigidity and triangularity of an exponential map

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}.

math.AC↗

arXiv2024

An Algebraic characterization of the affine three space in arbitrary characteristic

We give an algebraic characterization of the affine $3$-space over an algebraically closed field of arbitrary characteristic. We use this characterization to reformulate the following question. Let $$A=k[X, Y, Z, T]/(XY+Z^{p^e}+T+T^{sp})$$ where $p^e\nmid sp$, $sp\nmid p^e$, $e, s\geq 1$ and $k$ is an algebraically closed field of positive characteristic $p$. Is $A= k^{[3]}$? We prove some results on ML and ML$^*$ invariants and use them to prove a special case of the strong cancellation of $k^{[2]}$.

math.AC↗