Etale Steenrod手术和Artin-Tate配对
Etale Steenrod operations and the Artin-Tate pairing
摘要：
证明了1966年Tate关于有限域上曲面的Brauer群上的Artin-Tate配对的猜想，该猜想类似于Cassels-Tate配对.泰特问，如果这种配对总是交替和我们找到一个肯定的答案，这是有点令人惊讶的工作，Poonen斯托尔的卡塞尔-泰特配对。我们的方法是基于研究之间的连接的Artin-Tate配对和（推广）Steenrod操作在平展上同调。受类比流形的代数拓扑的启发，我们开发了工具，使我们能够计算相关的特征类的étale Steenrod操作。
英文摘要：
We prove a 1966 conjecture of Tate concerning the Artin-Tate pairing on the Brauer group of a surface over a finite field, which is the analogue of the Cassels-Tate pairing. Tate asked if this pairing is always alternating and we find an affirmative answer, which is somewhat surprising in view of the work of Poonen-Stoll on the Cassels-Tate pairing. Our method is based on studying a connection between the Artin-Tate pairing and (generalizations of) Steenrod operations in étale cohomology. Inspired by an analogy to the algebraic topology of manifolds, we develop tools allowing us to calculate the relevant étale Steenrod operations in terms of characteristic classes.
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