The $E_1$‐term of the (2‐local) $\mathrm{bo}$‐based Adams spectral sequence for the sphere spectrum decomposes into a direct sum of a $v_1$‐periodic part, and a $v_1$‐torsion part. Lellmann and Mahowald completely computed the $d_1$‐differential on the $v_1$‐periodic part, and the corresponding contribution to the $E_2$‐term. The $v_1$‐torsion part is harder to handle, but with the aid of a computer it was computed through the 20‐stem by Davis. Such computer computations are limited by the exponential growth of $v_1$‐torsion in the $E_1$‐term. In this paper, we introduce a new method for computing the contribution of the $v_1$‐torsion part to the $E_2$‐term, whose input is the cohomology of the Steenrod algebra. We demonstrate the efficacy of our technique by computing the $\mathrm{bo}$‐Adams spectral sequence beyond the 40‐stem.

中文翻译：

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关于bo-Adams光谱序列的E2项

的 ${Ë}_{\mathrm{1个}}$（2-本地）的术语 $\mathrm{博}$基于球面光谱的Adams光谱序列分解为a的直接和 $v_{\mathrm{1个}}$周期部分，以及 $v_{\mathrm{1个}}$扭转部分。Lellmann和Mahowald完全计算了$d_{\mathrm{1个}}$-在 $v_{\mathrm{1个}}$周期部分，以及对 ${Ë}_2$-术语。的$v_{\mathrm{1个}}$扭转零件较难处理，但借助计算机，它是由戴维斯（Davis）通过20杆计算的。此类计算机计算受到以下因素的指数增长的限制：$v_{\mathrm{1个}}$扭转 ${Ë}_{\mathrm{1个}}$-术语。在本文中，我们介绍了一种新的方法来计算$v_{\mathrm{1个}}$扭转部分 ${Ë}_2$-term，其输入是Steenrod代数的同调性。我们通过计算$\mathrm{博}$-40根以外的亚当光谱序列。