AI 中文总结
研究\(\Spin(10)\)的积分周环限制映射像，核心方法是构造类\(c_2c_3c_5\)，主要贡献是确定了模\(2\)和积分的周环特征标像，为相关研究提供关键结果。
AI 中文摘要
设\(G = \Spin(10)\)是特征不为\(2\)的域上的分裂旋群，\(T\subset G\)是分裂极大环面。我们确定积分周环限制映射\(\CH(BG)\to \CH(BT)^W\)的像，即\(\CH(BG)\)模挠。证明中的主要新几何要素是类\(c_2c_3c_5\)的构造，其中\(c_i\)是限制到\(T\)后的初等陈类。该类由与特殊克利福德群\(\Gamma^+(10)\)的半旋嵌入中的旋量簇上的仿射锥相关的恰当等变前推得到。模\(2\)时，像是由\(\F[c_2,c_3,c_4,c_5]\)中包含\(c_2^2,c_3^2,c_4^2,c_5\)和\(c_2c_3c_5\)的最小斯廷罗德稳定子环上，半旋表示的最高陈类的环面限制生成的子环。积分特征标像是这个模\(2\)子环在模\(2\)约化下的完全原像。
英文摘要
Let \(G=\Spin(10)\) be the split spin group over a field of characteristic different from \(2\), and let \(T\subset G\) be a split maximal torus. We determine the image of the integral Chow restriction map \(\CH(BG)\to \CH(BT)^W\), equivalently \(\CH(BG)\) modulo torsion. The main new geometric ingredient in the proof is a construction of the class \(c_2c_3c_5\), where the \(c_i\) are the elementary Chern classes after restriction to \(T\). This class is obtained from the proper equivariant push-forward associated with the affine cone over the spinor variety in its half-spin embedding for the special Clifford group \(Γ^+(10)\). Modulo two, the image is the subring generated, over the smallest Steenrod-stable subring of \(\F[c_2,c_3,c_4,c_5]\) containing \(c_2^2,c_3^2,c_4^2,c_5\) and \(c_2c_3c_5\), by the torus restriction of the top Chern class of a half-spin representation. The integral characteristic image is the full inverse image of this mod-two subring under reduction modulo \(2\).
