论文标题
$ C_1 $猜想的混合特征的病理案例
A pathological case of the $C_1$ conjecture in mixed characteristic
论文作者
论文摘要
令$ k $为特征0。修复整数$ r，d $ coprime，带有$ r \ geq 2 $。令$ x_k $为平滑，投射，几何连接的曲线，$ g \ geq 2 $定义了K。在本文中，我们证明存在$ x_k $的本地自由捆，带等级$ r $和clistant $ l_k $。这在微不足道的情况下证明了$ c_1 $在混合特征中的$ C_1 $猜想，用于在平滑，投影曲线上具有固定等级的稳定稳定带皮带的模量空间。
Let $K$ be a field of characteristic 0. Fix integers $r,d$ coprime with $r \geq 2$. Let $X_K$ be a smooth, projective, geometrically connected curve of genus $g \geq 2$ defined over K. Assume there exists a line bundle $L_K$ on $X_K$ of degree $d$. In this article we prove the existence of a stable locally free sheaf on $X_K$ with rank $r$ and determinant $L_K$. This trivially proves the $C_1$ conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve.
