arXiv math/00021312000-02-16math.KTmath.OA

Chern character for the Schwartz algebra of p-adic GL(n)

Jacek Brodzki, Roger Plymen

英文摘要：

We construct a Chern character map from the K-theory of the reduced C^* algebra of the p-adic GL(n) with values in the periodic cyclic homology of the Schwartz algebra of this group. We prove that this map is an isomorphism after tensoring with C by comparing an explicit formula, stated in the algebraic case by Cuntz and Quillen, with the classical Chern character. This Chern character is a crucial ingredient in the proof of the Baum-Connes conjecture for the p-adic GL(n) due to Baum, Higson and Plymen.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

On syntomic regulators I: constructions

We show that classical Chern classes from higher ($p$-adic) $K$-theory to syntomic cohomology extend to logarithmic syntomic cohomology. These Chern classes are compatible -- in a suitable sense -- with addition, products, and $λ$-operations. They are also compatible with the canonical Gysin sequences and, via period maps, with logarithmic étale Chern classes. Moreover, they induce logarithmic crystalline Chern classes. This uses as a critical new ingredient the recent comparison of syntomic cohomology with $p$-adic nearby cycles and $p$-adic motivic cohomology.

2016-07-18math.AGmath.KTmath.NT

The Relative Chern Character and Regulators

In this thesis we construct a modified version of Karoubi's relative Chern character for smooth varieties over the complex numbers or the ring of integers in a p-adic number field. Comparison results with the Deligne-Beilinson Chern character and the p-adic Borel regulator constructed by Huber and Kings are proven. As a corollary we obtain a new proof of Burgos' theorem that Borel's regulator is twice Beilinson's regulator.

2010-07-08math.AGmath.KTmath.NT

Some Fréchet algebras for which the Chern character is an isomorphism

Using similarities between topological $K$-theory and periodic cyclic homology we show that, after tensoring with $\mathbb C$, for certain Fréchet algebras the Chern character provides an isomorphism between these functors. This is applied to prove that the Hecke algebra and the Schwartz algebra of a reductive $p$-adic group have isomorphic periodic cyclic homology. The main theorem in the first version was incorrect for algebras related to noncompact manifolds. This has no effect on the results concerning p-adic groups. In the appendix we show that an analogous cohomological result does hold …

2008-09-29math.KT

Periodic cyclic homology of reductive p-adic groups

Let G be a reductive p-adic group, H(G) its Hecke algebra and S(G) its Schwartz algebra. We will show that these algebras have the same periodic cyclic homology. This might be used to provide an alternative proof of the Baum-Connes conjecture for G, modulo torsion. As preparation for our main theorem we prove two results that have independent interest. Firstly a general comparison theorem for the periodic cyclic homology of finite type algebras and certain Fréchet completions thereof. Secondly a refined form of the Langlands classification for G, which clarifies the relation between the smooth…

2009-06-29math.KTmath.RT

Periodicity and the determinant bundle

The infinite matrix `Schwartz' group $G^{-\infty}$ is a classifying group for odd K-theory and carries Chern classes in each odd dimension, generating the cohomology. These classes are closely related to the Fredholm determinant on $G^{-\infty}.$ We show that while the higher (even, Schwartz) loop groups of $G^{-\infty},$ again classifying for odd K-theory, do \emph{not} carry multiplicative determinants generating the first Chern class, `dressed' extensions, corresponding to a star product, do carry such functions. We use these to discuss Bott periodicity for the determinant bundle and the et…

2006-06-16math.DGmath.KT

Karoubi's relative Chern character, the rigid syntomic regulator, and the Bloch-Kato exponential map

We construct a variant of Karoubi's relative Chern character for smooth, separated schemes over the ring of integers in a p-adic field and prove a comparison with the rigid syntomic regulator. For smooth projective schemes we further relate the relative Chern character to the etale p-adic regulator via the Bloch-Kato exponential map. This reproves a result of Huber and Kings for the spectrum of the ring of integers and generalizes it to all smooth projective schemes as above.

2014-07-21math.AGmath.KTmath.NT

更多相关论文收起更多论文

约化 p-adic 群的群代数、其表示及其非交换几何

Group algebras of reductive $p$-adic groups, their representations and their noncommutative geometry

本文综述约化 p-adic 群的 Hecke、Schwartz 与约化 C*-代数结构、表示分类及 K-理论，并给出包含挠元素的 $K_*(C_r^*(G))$ 新计算。

2025-10-20math.KTmath.RT

约化 $p$-进群的 Hochschild 同调

Hochschild homology of reductive $p$-adic groups

本文研究约化 $p$-进群的 Hecke 与 Harish-Chandra–Schwartz 代数，利用光滑表示族和 Bernstein 分解证明其 Hochschild、循环同调与交叉积代数对应，并联系 K-理论。

2025-01-17math.KTmath.RT