论文标题
关于第一个史密斯 - 河托谱系中同质物中β和伽马元素的产品
On products of beta and gamma elements in the homotpy of the first Smith-Toda spectrum
论文作者
论文摘要
在本文中，我们确定了单色comodule $ m^1_2 $在奇数上的第一个共同体，并将结果应用于在史密斯 - 大硫醇谱$ v（1）$的同型群体中显示某些Beta和Gamma元素的某些产品的非平价。第一作者确定了大于三个的素数的同时学。在这里，我们通过基本计算来验证它们并确定Prime 3处的共同体。该协同学将是计算单色comodule $ m^3_0 $的协同组的垫脚石，我们希望很长一段时间来确定。
In this paper, we determine the first cohomology of the monochromatic comodule $M^1_2$ at an odd prime, and apply the results to show non-trivialities of some products of beta and gamma elements in the homotopy groups of the Smith-Toda spectrum $V(1)$. The cohomology for a prime greater than three was determined by the first author. Here, we verify them and determine the cohomology at the prime 3 by elementary calculation. The cohomology will be a stepping stone for computing the cohomology of the monochromatic comodule $M^3_0$, which we hope to determine for a long time.
