THE RIGID SYNTOMIC RING SPECTRUM
THE RIGID SYNTOMIC RING SPECTRUM
复制标题
刚性合成环谱
DOI：
10.1017/s1474748014000152
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发表时间：
2012
影响因子：
0.9
通讯作者：
Nicola Mazzari
中科院分区：
文献类型：
--
作者：
Fr'ed'eric D'eglise;Nicola Mazzari
本文的目的是表明，刚性同伦上同调-定义的Besser -是由一个合理的环谱的motivic同伦意义。事实上，扩展以前的建设，我们表现出一个简单的可表示性标准，我们将其应用到几个上同调，以得到我们的中心结果。这个定理给出了刚性同分上同调的新结果，如h-下降和Gysin态射的圈类的相容性。沿着的方式，我们证明了motivic环谱诱导一个完整的Bloch-Ogus上同调形式主义，甚至更多。最后，遵循一般的动机同伦哲学，我们展示了一个自然的概念，刚性同分系数。
The aim of this paper is to show that rigid syntomic cohomology – defined by Besser – is representable by a rational ring spectrum in the motivic homotopical sense. In fact, extending previous constructions, we exhibit a simple representability criterion and we apply it to several cohomologies in order to get our central result. This theorem gives new results for rigid syntomic cohomology such as h-descent and the compatibility of cycle classes with Gysin morphisms. Along the way, we prove that motivic ring spectra induce a complete Bloch–Ogus cohomological formalism and even more. Finally, following a general motivic homotopical philosophy, we exhibit a natural notion of rigid syntomic coefficients.