Adams谱序列中的两个非平凡微分

Two Nontrivial Differentials in the Adams Spectral Sequence

令p≥5为奇素数,研究Adams谱序列的二阶微分d_2:Ext_A^(*,*)(Z_p,Z_p)→Ext_A^(*+2,*+1)(Z_p,Z_p),得到两个非平凡微分d_2(gi)=a_0l_i与d_2(k_i)=a_0l′_i,其中g_i∈Ext_A^(2,(p^(i+1)+2p^i)q)(Z_p,Z_p),k_i∈Ext_A^(2,(p^(i+1)+p^i)q)(Z_p,Z_p),a_0∈Ext_A^(1,1)(Z_p,Z_p), l_i∈Ext_A^(3,(p^(i+1)+2p^i)q)(Z_p,Z_p),l′_i∈Ext_A^(3,(2p^(i+1)+p^i)q)(Z_p,Z_p),q=2(p-1),i>0.

Let p≥5 be an odd prime,this paper studies the secondary differential d2： ExtA^＊,＊（Zp,Zp）→ExtA^＊＋2,＊＋1（Zp,Zp） in the Adams spectral sequence to get two nontrivial differentials which are d2（gi）=a0li and d2（ki）=a0l′i,where gi∈ExtA^2,（p^i＋1＋2p^i）q（Zp,Zp）,ki∈ExtA^2,（2p^i＋1＋p^i）q）（Zp,Zp）,a0∈ExtA^1,1（Zp,Zp）,li∈ExtA^3,（p^i＋1＋2p^i）q（Zp,Zp）,l′i∈ExtA^3,（2p^i＋1＋p^i）q（Zp,Zp）,q=2（p-1）,i〉0.