Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0707.3682

On the p-adic Beilinson conjecture for number fields

Amnon Besser·Paul Buckingham·Rob de Jeu·Xavier-Francois Roblot
View original source ↗Read source document ↗Export metadata ↓

Abstract

We formulate a conjectural p-adic analogue of Borel's theorem relating regulators for higher K-groups of number fields to special values of the corresponding zeta-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresponding conjecture for Artin motives, and state a conjecture about the precise relation between the p-adic and classical situations. Parts of he conjectures are proved when the number field (or Artin motive) is Abelian over the rationals, and all conjectures are verified numerically in some other cases.

Explore related subjects

math.KTmath.NT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Amnon Besser, Paul Buckingham, Rob de Jeu, Xavier-Francois Roblot. 2007-11-19. On the p-adic Beilinson conjecture for number fields. https://arxiv.org/abs/0707.3682

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

$E$-theory is compactly assembled

We show that the equivariant $E$-theory category $\mathrm{E}_{\mathrm{sep}}^{G}$ for separable $C^{*}$-algebras is a compactly assembled stable $\infty$-category. We derive this result as a consequence of the shape theory for $C^{*}$-algebras developed by Blackadar and Dardarlat and a new construction of $\mathrm{E}_{\mathrm{sep}}^{G}$. As an application we investigate a topological enrichment of the homotopy category of a compactly assembled $\infty$-category in general and argue that the results of Carrión and Schafhauser on the enrichment of the classical $E$-theory category can be derived by specialization.

math.KT↗
arXiv2026

Scissors automorphism groups I: Homological stability and K-theory

In any category with a reasonable notion of cover, each object has a group of scissors automorphisms. We prove that under mild conditions, the homology of this group is independent of the object, and can be expressed in terms of the scissors congruence K-theory spectrum defined by Zakharevich. We therefore obtain both a group-theoretic interpretation of Zakharevich's higher scissors congruence K-theory, as well as a method to compute the homology of scissors automorphism groups. In the classical case of scissors congruence of polytopes, this leads to calculations and structural results on the homology of the scissors automorphism group. In two sequels, we show that more generally our approach leads to homology calculations for various families of groups appearing in group theory and dynamics, recovering results of Szymik-Wahl, Li, and Tanner.

math.KT↗