Chern子环的谱
The spectrum of the Chern subring
摘要：
对于紧李群的模p上同调环的某些子环，我们给出了素理想谱的描述，类似于Quillen对全环谱的描述.这样的子环的例子包括陈子环（由所有酉表示的陈类生成的子环），以及对于有限群，由在任何指定域上可实现的表示的陈类生成的子环。作为推论，我们得到了紧李群G的上同调环包含Chern子环是F-同构当且仅当下列条件成立：对于G的任意初等交换p-子群之间的同态f，使得f（v）总是共轭于v，存在G的元素g，使得f等于g的共轭.
英文摘要：
For certain subrings of the mod-p cohomology ring of a compact Lie group, we give a description of the prime ideal spectrum, analogous to Quillen's description of the spectrum of the whole ring. Examples of such subrings include the Chern subring (the subring generated by Chern classes of all unitary representations), and for finite groups the subring generated by Chern classes of representations realizable over any specified field. As a corollary, we deduce that the inclusion of the Chern subring in the cohomology ring is an F-isomorphism for a compact Lie group G if and only if the following condition holds: For any homomorphism f between elementary abelian p-subgroups of G such that f(v) is always conjugate to v, there is an element g of G such that f is equal to conjugation by g.
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