论文标题
亚当斯操作的里曼 - 罗奇定理
The Riemann-Roch theorem for the Adams operations
论文作者
论文摘要
We prove the classical Riemann-Roch theorems for the Adams operations $\,ψ^j\,$ on $K$-theory: a statement with coefficients on $\mathbb{Z}[j^{-1}]$, that holds for arbitrary projective morphisms, as well as another one with integral coefficients, that is valid for closed immersions.在存在有理系数的情况下，我们还分析了一个ADAMS操作的相应Riemann-Roch公式与Chern特征的类似公式之间的关系。 为此，我们完成了Panin-Smirnov的作品的基本阐述，该作品是由第一作者在以前的作品中发起的。他们对代数品种的定向共同体学理论的概念允许使用经典论证来证明一般和整洁的陈述，这意味着上述所有结果是特定情况。
We prove the classical Riemann-Roch theorems for the Adams operations $\,ψ^j\,$ on $K$-theory: a statement with coefficients on $\mathbb{Z}[j^{-1}]$, that holds for arbitrary projective morphisms, as well as another one with integral coefficients, that is valid for closed immersions. In presence of rational coefficients, we also analyze the relation between the corresponding Riemann-Roch formula for one Adams operation and the analogous formula for the Chern character. To do so, we complete the elementary exposition of the work of Panin-Smirnov that was initiated by the first author in a previous work. Their notion of oriented cohomology theory of algebraic varieties allows to use classical arguments to prove general and neat statements, which imply all the aforementioned results as particular cases.
