关于tmf在素数2处的Tate谱
On the Tate spectrum of tmf at the prime 2
摘要：
涉及根不变量的计算促使Mahowald和Shick提出了这样的口号：“v_n周期同伦的根不变量是v_n挠率。虽然文献中既没有证据，也没有对这一口号的精确陈述，但许多作者提供了计算证据来支持其基本思想。根不变量与Mahowald对Tate谱的逆极限描述密切相关，计算表明v_n周期上同调理论的Tate谱是v_n挠的.本文的目的是分裂的泰特频谱tmf作为一个楔子的悬浮液的kO，提供另一个例子，支持口号，以现有的文献。
英文摘要：
Computations involving the root invariant prompted Mahowald and Shick to develop the slogan: "the root invariant of v_n periodic homotopy is v_n torsion." While neither a proof, nor a precise statement, of this slogan appears in the literature, numerous authors have offered computational evidence in support of its fundamental idea. The root invariant is closely related to Mahowald's inverse limit description of the Tate spectrum, and computations have shown the Tate spectrum of v_n periodic cohomology theories to be v_n torsion. The purpose of this paper is to split the Tate spectrum of tmf as a wedge of suspensions of kO, providing yet another example in support of the slogan to the existing literature.
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