Minimal polynomial of an exponential automorphism of C^n

特征 p>0 下 $\bf A^n$ 的 p 阶自同构的指数性

On exponentiality of automorphisms of ${\bf A}^n$ of order $p$ in characteristic $p>0$

本文研究正特征仿射空间 $\bf A_R^n$ 中 $p$ 阶自同构能否由 $\bf G_a$-作用诱导，证明低维三角情形、构造非指数例子并分析初等自同构。

Exponential automorphisms and a problem of Mycielski

An exponential automorphism of $\mathbf{C}$ is a function $α: \mathbf{C} \rightarrow \mathbf{C}$ such that $α(z_1 + z_2) = α(z_1) + α(z_2)$ and $α\left( e^z \right) = e^{α(z)}$ for all $z, z_1, z_2 \in \mathbf{C}$. Jan Mycielski asked if $α(\ln 2) = \ln 2$ and if $α(2^{1/k}) = 2^{1/k}$ for $k = 2, 3, 4$ and for all exponential automorphisms $α$. These questions are answered modulo a multiple of $2πi$ and a root of unity.

A non-tame and non-co-tame automorphism of the polynomial ring

An automorphism $F$ of the polynomial ring in $n$ variables over a field of characteristic zero is said to be {\it co-tame} if the subgroup of the automorphism group of the polynomial ring generated by $F$ and affine automorphisms contains the tame subgroup. There exist many examples of such an $F$, and several sufficient conditions for co-tameness are already known. In 2015, Edo-Lewis gave the first example of a non-cotame automorphism, which is a tame automorphism of the polynomial ring in three variables. In this paper, we give the first example of a non-cotame automorphism which is not tam…

双分次微分代数的障碍理论

Obstruction Theory for Bigraded Differential Algebras

本文发展了带扭曲系数的cbba的Hirsch扩张的障碍理论，并应用于极小cbba的结构定理、相对极小模型的构造与唯一性，以及自同构群和形式性的刻画。