二次型对商环谱上的乘积进行分类
Quadratic forms classify products on quotient ring spectra
摘要：
本文构造了双线性型群Bil（I/I^2[1]）在F上的R-乘积集上的自由传递作用，F是E-无限环谱R与F_* \cong R_*/I的正则商.我们证明了这个作用诱导了二次型QF（I/I^2[1]）在F上R-积的等价类集合上的自由传递作用。作者在前一篇文章中引入的F的特征双线性型是F交换性的自然障碍。我们讨论了Morava K-理论K（n）和2-周期Morava K-理论K_n的例子。
英文摘要：
We construct a free and transitive action of the group of bilinear forms Bil(I/I^2[1]) on the set of R-products on F, a regular quotient of an E-infinity ring spectrum R with F_* \cong R_*/I. We show that this action induces a free and transitive action of the group of quadratic forms QF(I/I^2[1]) on the set of equivalence classes of R-products on F. The characteristic bilinear form of F introduced by the authors in a previous paper is the natural obstruction to commutativity of F. We discuss the examples of the Morava K-theories K(n) and the 2-periodic Morava K-theories K_n.
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