论文标题
$ C_1 $ - 场上简单滑轮的下降理论
Descent theory of simple sheaves on $C_1$-fields
论文作者
论文摘要
让$ k $为任何特征的$ C_1 $ - $ x $ a投射品种超过$ k $。在本文中，我们证明，对于有限的Galois扩展名$ L $ K $的$ L $，这是一个简单的捆，并在$ x \ times_k l $上覆盖基准，以$ x $上的简单链条下降。结果，我们表明，与固定的Hibert Polyenmial $ P $的$ x $上的几何稳定束带和相应模量空间的$ K $ - 差异点之间有$ 1-1 $的对应关系。
Let $K$ be a $C_1$-field of any characteristic and $X$ a projective variety over $K$. In this article we prove that for a finite Galois extension $L$ of $K$, a simple sheaf with covering datum on $X \times_K L$ descends to a simple sheaf on $X$. As a consequence, we show that there is a $1-1$ correspondence between the set of geometrically stable sheaves on $X$ with fixed Hibert polynomial $P$ and the set of $K$-rational points of the corresponding moduli space.
