论文标题
在对称双线性形式的Witt环中分开的力量
Divided powers in the Witt ring of symmetric bilinear forms
论文作者
论文摘要
对称双线性形式在一个场上形成的Witt环将功率操作分开。另一方面，它遵循加里波第 - 梅尔库杰夫·塞尔（Garibaldi-Merkurjev-Serre）在同一个不变的方面的作品，即所有在维特环上的操作本质上都是外部力量的线性组合。我们发现分裂力的明确公式是外部力量的线性组合。系数涉及``切线数字''，与伯努利数字有关。 Witt环上的分开的力量为Milnor K理论Modulo 2的分裂力量提供了另一个结构。
The Witt ring of symmetric bilinear forms over a field has divided power operations. On the other hand, it follows from Garibaldi-Merkurjev-Serre's work on cohomological invariants that all operations on the Witt ring are essentially linear combinations of exterior powers. We find the explicit formula for the divided powers as a linear combination of exterior powers. The coefficients involve the ``tangent numbers'', related to Bernoulli numbers. The divided powers on the Witt ring give another construction of the divided powers on Milnor K-theory modulo 2.
