The hyperring of adèle classes
The hyperring of adèle classes
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阿黛尔班的超级环
DOI：
10.1016/j.jnt.2010.09.001
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发表时间：
2011
影响因子：
0.7
通讯作者：
C. Consani
中科院分区：
文献类型：
--
作者：
A. Connes;C. Consani
我们证明了超环理论，由于M。Krasner等人的研究为理解整体域K的Adèle类空间HK=AK/K×的代数结构提供了一个完美的框架。在将F1推广到超域K之后，我们证明了R/G形式的超环（其中R是环，G <$R×是其乘法群的子群）是K的超环扩张当且仅当G <${0}是R的子域.这个结果适用于adèle类空间，从而继承了K的超环扩张HK的结构。我们开始研究K上代数几何的内容。K的交换超环扩张范畴包括：域上具有半线性同态的交换代数、具有内射同态的阿贝尔群和包含齐次非Desklesian平面的奇异地。最后，我们证明了对于正特征的整体域K，超环HK的素元的广群与整体域K的曲线的极大交换覆盖的环的广群是正则等变同构的.视频：有关本文的视频摘要，请单击此处或访问http://www.youtube.com/watch? v=3LSKD_PfJyc。
TEXT: We show that the theory of hyperrings, due to M. Krasner, supplies a perfect framework to understand the algebraic structure of the adèle class space HK=AK/K×of a global field K. After promoting F1to a hyperfield K, we prove that a hyperring of the form R/G (where R is a ring and G⊂R×is a subgroup of its multiplicative group) is a hyperring extension of K if and only if G∪{0} is a subfield of R. This result applies to the adèle class space which thus inherits the structure of a hyperring extension HKof K. We begin to investigate the content of an algebraic geometry over K. The category of commutative hyperring extensions of K is inclusive of: commutative algebras over fields with semi-linear homomorphisms, abelian groups with injective homomorphisms and a rather exotic land comprising homogeneous non-Desarguesian planes. Finally, we show that for a global field K of positive characteristic, the groupoid of the prime elements of the hyperring HKis canonically and equivariantly isomorphic to the groupoid of the loops of the maximal abelian cover of the curve associated to the global field K. VIDEO: For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=3LSKD_PfJyc.
绝对导数和 zeta 函数
DOI：
--
发表时间：
2003
期刊：
Doc.Math. Extra Vol.
影响因子：
--
作者：
N.Kurokawa;H.Ochiai;M.Wakayama
通讯作者：
M.Wakayama