论文标题
$ g $ - 代数的模量空间
The moduli space of $G$-algebras
论文作者
论文摘要
让$ l $是Galois代数，带有Galois Group $ g $，让$ x $是$ l $的普通元素。 Moduli Space $ \ Mathcal x $ Pairs $（L，X）$是对商的开放子集$ \ Mathbb p/g $的同构，其中$ \ Mathbb p $是$ g $常规表示的投射空间。我们为在$ l $ $ l $的代数不变式和$ x $的代数不变的$ \ mathbb p/g $的天然adelic指标方面提供了任何对$ $（l，x）\ in \ mathcal x（\ mathbb q）$的高度的公式。
Let $L$ be a Galois algebra with Galois group $G$ and let $x$ be a normal element of $L$. The moduli space $\mathcal X$ of pairs $(L,x)$ is isomorphic to an open subset of the quotient variety $\mathbb P/G$, where $\mathbb P$ is the projective space of the regular representation of $G$. We provide a formula for the height of any pair $(L,x) \in \mathcal X(\mathbb Q)$ in terms of algebraic invariants of $L$ and $x$ with respect to a natural adelic metric on the anticanonical divisor of $\mathbb P/G$.
