bc系统,绝对环切术和量子化微积分

IF 1.3 Q1 MATHEMATICS
Alain Connes, Caterina Consani
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引用次数: 1

摘要

我们对bc系统的几个发展进行了简短的调查,理性的阿黛尔类空间,以及对后者空间的“泽塔部门”作为尺度站点的理解。我们给出的新结果将bc -系统描述为绝对基$\mathbb{S}$的“代数闭包”的泛威特环(即$K$-自同态理论)。通过这种方法,我们在最基本的代数水平上获得了BC动力系统的概念意义。进一步,我们定义了一维Schwartz核的不变量,并将傅里叶变换(一维)与其在代数闭包$\mathbb{S}$上的作用联系起来。我们实现这个不变量是为了证明,当应用于一个函数的量子化微分时,它提供了它的Schwarzian导数。最后,我们研究了量子化微积分与Weil的正相关的作用,以及谱三元组与黎曼ζ函数的零点相关的作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
BC-system, absolute cyclotomy and the quantized calculus
We give a short survey on several developments on the BC-system, the adele class space of the rationals, and on the understanding of the"zeta sector"of the latter space as the Scaling Site. The new result that we present concerns the description of the BC-system as the universal Witt ring (i.e. K-theory of endomorphisms) of the"algebraic closure"of the absolute base S. In this way we attain a conceptual meaning of the BC dynamical system at the most basic algebraic level. Furthermore, we define an invariant of Schwartz kernels in 1 dimension and relate the Fourier transform (in 1 dimension) to its role over the algebraic closure of S. We implement this invariant to prove that, when applied to the quantized differential of a function, it provides its Schwarzian derivative. Finally, we survey the roles of the quantized calculus in relation to Weil's positivity, and that of spectral triples in relation to the zeros of the Riemann zeta function.
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
4
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