论文标题
正常品种的零周期
Zero-cycles on normal varieties
论文作者
论文摘要
我们证明了Kato-Saito阶级域理论的扩展，用于在有限的领域到具有奇异性方案的有限领域的光滑投射方案。作为应用程序，我们获得了此类方案上0循环的Chow组Bloch的公式。我们在代数封闭的磁场上，在其常规基因座的SUSLIN同源性上确定了0个循环的ChOW组。我们的最终结果是在代数闭合场上平滑准标记方案的Roitman Torsion定理。这完成了Spiess和Szamuely扭转定理中缺失的$ p $ torsion部分。
We prove an extension of the Kato-Saito class field theory for smooth projective schemes over a finite field to schemes with singularities. As an application, we obtain Bloch's formula for the Chow groups of 0-cycles on such schemes. We identify the Chow group of 0-cycles on a normal projective scheme over an algebraically closed field to the Suslin homology of its regular locus. Our final result is a Roitman torsion theorem for smooth quasi-projective schemes over algebraically closed fields. This completes the missing $p$-torsion part in the torsion theorem of Spiess and Szamuely.
