结构环谱的Smith理想

摘要：

在Jeff Smith的基础上，我们发展了对称么半群模型范畴中么半群理想的同伦理论。这包括史密斯理想的结构环谱和微分分次代数。这样的史密斯理想不是次优的，因此这个理论似乎要求我们同时考虑所有么半群的所有史密斯理想，而不是局限于一个特定么半群的史密斯理想。然而，我们可以通过Smith理想取商，得到幺半群同态。在稳定的情况下，我们表明，这种结构是一个模型范畴的史密斯理想和模型范畴的幺半群同态之间的奎伦等价的一部分。

英文摘要：

Pursuing ideas of Jeff Smith, we develop a homotopy theory of ideals of monoids in a symmetric monoidal model category. This includes Smith ideals of structured ring spectra and of differential graded algebras. Such Smith ideals are NOT subobjects, and as a result the theory seems to require us to consider all Smith ideals of all monoids simultaneously, rather then restricting to the Smith ideals of one particular monoid. However, we can take a quotient by a Smith ideal and get a monoid homomorphism. In the stable case, we show that this construction is part of a Quillen equivalence between a model category of Smith ideals and a model category of monoid homomorphisms.

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