关于谱的循环不动点
On cyclic fixed points of spectra
摘要：
对于有限p-群G和有限型mod p的下有界G-谱X，X的G-等变Segal猜想断言：正则映射X^G --> X^{hG}是p-adic等价。设C_{p^n}是阶为p^n的循环群.本文证明了，如果C_p Segal猜想对C_{p^n}谱X成立，并且对X的每个C_{p^e}几何不动点成立（0 < e < n），则C_{p^n} Segal猜想对X成立.类似的结果也适用于较弱形式的西格尔猜想，只要求正则映射在具有适当有限系数的同伦群上诱导足够高次数的等价。
英文摘要：
For a finite p-group G and a bounded below G-spectrum X of finite type mod p, the G-equivariant Segal conjecture for X asserts that the canonical map X^G --> X^{hG} is a p-adic equivalence. Let C_{p^n} be the cyclic group of order p^n. We show that if the C_p Segal conjecture holds for a C_{p^n} spectrum X, as well as for each of its C_{p^e} geometric fixed points for 0 < e < n, then then C_{p^n} Segal conjecture holds for X. Similar results hold for weaker forms of the Segal conjecture, asking only that the canonical map induces an equivalence in sufficiently high degrees, on homotopy groups with suitable finite coefficients.
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