G. Kings

activity

19972026

most citedRankin--Eisenstein classes and explicit reciprocity laws

109 citations · 267 across the 22 of their papers we have counts for

collaborators

26 papers

math.NT2026

$p$ -adic $L$ -functions for Hecke characters of totally imaginary fields

Guido Kings, Johannes Sprang

We construct $p$ -adic $L$ -functions interpolating critical $L$ -values of algebraic Hecke characters for arbitrary unramified primes $p$ and any totally imaginary field. For non-ord…

math.NT2025

Algebraicity of critical Hecke $L$ -values

Guido Kings, Johannes Sprang

In this survey, we review the known results on the algebraicity of critical values of Hecke $L$ -functions and explain the new developments in \cite{Kings-Sprang}.

math.NT2024

Another look at $p$ -adic Fourier-theory

Guido Kings, Johannes Sprang

In this short note, we show that a natural generalization of the $p$ -adic Fourier theory of Schneider and Teitelbaum follows immediately from the classification of $p$ -divisible gr…

math.NT2019★ 5 cited

Eisenstein-Kronecker classes, integrality of critical values of Hecke $L$ -functions and $p$ -adic interpolation

Guido Kings, Johannes Sprang

We show that for an arbitrary totally complex number field $L$ the (regularized) critical $L$ -values of algebraic Hecke characters of $L$ divided by certain periods are algebraic i…

math.AG2018

The Maillot-Rössler current and the polylogarithm on abelian schemes

Guido Kings, Danny Scarponi

We give a conceptual proof of the fact that the realisation of the degree zero part of the polylogarithm on abelian schemes in analytic Deligne cohomology can be described in terms…

math.NT2015

On $p$ -adic interpolation of motivic Eisenstein classes

Guido Kings

In this paper we prove that the motivic Eisenstein classes associated to polylogarithms of commutative group schemes can be $p$ -adically interpolated in étale cohomology. This gene…

math.AG2015★ 10 cited

Polylogarithm for families of commutative group schemes

Annette Huber, Guido Kings

We generalize the definition of the polylogarithm classes to the case of commutative group schemes, both in the sheaf theoretic and the motivic setting. This generalizes and simpli…

math.NT2015★ 109 cited

Rankin--Eisenstein classes and explicit reciprocity laws

Guido Kings, David Loeffler, Sarah Livia Zerbes

We construct three-variable $p$ -adic families of Galois cohomology classes attached to Rankin convolutions of modular forms, and prove an explicit reciprocity law relating these cl…

math.NT2015★ 46 cited

Rankin--Eisenstein classes for modular forms

Guido Kings, David Loeffler, Sarah Livia Zerbes

In this paper we make a systematic study of certain motivic cohomology classes ("Rankin-Eisenstein classes") attached to the Rankin--Selberg convolution of two modular forms of wei…

math.AG2014

Higher analytic torsion, polylogarithms and norm compatible elements on abelian schemes

Guido Kings, Damian Rössler

We give a simple axiomatic description of the degree 0 part of the polylogarithm on abelian schemes and show that its realisation in analytic Deligne cohomology can be described in…

math.NT2014★ 22 cited

Topological polylogarithms and $p$ -adic interpolation of $L$ -values of totally real fields

Alexander Beilinson, Guido Kings, Andrey Levin

We develop the topological polylogarithm which provides an integral version of Nori's Eisenstein cohomology classes for $G L_{n} (Z)$ and yields classes with values in an Iwas…

math.NT2014★ 10 cited

Rankin-Selberg Euler systems and p-adic interpolation

Guido Kings, David Loeffler, Sarah Livia Zerbes

We construct motivic cohomology classes attached to Rankin--Selberg convolutions of modular forms of weights $\geq 2$ , show that these vary analytically in p-adic families, and rela…

math.NT2013★ 2 cited

Eisenstein classes, elliptic Soulé elements and the $ℓ$ -adic elliptic polylogarithm

Guido Kings

This is a completely rewritten version of the paper formerly entitled "Sheaves of Iwasawa modules, moment maps and the $ℓ$ -adic elliptic polylogarithm". The proof of the main re…

math.NT2010★ 5 cited

$p$ -adic Beilinson conjecture for ordinary Hecke motives associated to imaginary quadratic fields

Kenichi Bannai, Guido Kings

The purpose of this article is to give an overview of the series of papers [BK1], [BK2] concerning the $p$ -adic Beilinson conjecture of motives associated to Hecke characters of an…

math.NT2009

A cohomological Tamagawa number formula

Annette Huber, Guido Kings

For smooth linear group schemes over $Z$ we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa me…

math.NT2009★ 14 cited

Some complements to the Lazard isomorphism

Annette Huber, Guido Kings, Niko Naumann

Lazard showed in his seminal work "Groupes analytiques $p$ -adiques" that for rational coefficients continuous group cohomology of $p$ -adic Lie-groups is isomorphic to Lie-algebra c…

math.NT2008★ 1 cited

On the equivariant and the non-equivariant main conjecture for imaginary quadratic fields

Jennifer Johnson-Leung, Guido Kings

The Iwasawa main conjecture fields has been an important tool to study the arithmetic of special values of $L$ -functions of Hecke characters of imaginary quadratic fields. To obtai…

math.AG2007

A note on polylogarithms on curves and abelian schemes

Guido Kings

In this note we investigate the connection between polylogarithms on curves and abelian schemes. The main result shows that the polylogarithm on the abelian scheme can be obtained…

math.NT2007

p-adic elliptic polylogarithm, p-adic Eisenstein series and Katz measure

Kenichi Bannai, Guido Kings

The specializations of the motivic elliptic polylog are called motivic Eisenstein classes. For applications to special values of L-Functions, it is important to compute the realiza…

math.NT2006

A $p$ -adic analogue of the Borel regulator and the Bloch-Kato exponential map

Annette Huber, Guido Kings

In this paper we define a $p$ -adic analogue of the Borel regulator for the $K$ -theory of $p$ -adic fields. The van Est isomorphism in the construction of the classical Borel regulat…

math.NT2005

Degeneration of polylogarithms and special values of L-functions for totally real fields

Guido Kings

Replaced by revised version.

math.NT2004

On non-commutative twisting in etale and motivic cohomology

J. Hornbostel, G. Kings

In this paper we use ideas of the non-abelian Iwasawa main conjecture to prove a result about the first Galois cohomology of continuous Galois modules V_p(j) for large Tate-twist j…

math.NT2002★ 23 cited

Equivariant Bloch-Kato conjecture and non-abelian Iwasawa Main Conjecture

Annette Huber, Guido Kings

This is a contribution to the ICM 2002. We explain the relation between the (equivariant) Bloch-Kato conjecture for special values of L-functions and the Main Conjecture of (non-ab…

math.AG2001★ 1 cited

Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters

Annette Huber, Guido Kings

This is the completely revised version of math.AG/0101071.

p-adic L-functions for Hecke characters of totally imaginary fields

Algebraicity of critical Hecke L-values

Another look at p-adic Fourier-theory

Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation

The Maillot-Rössler current and the polylogarithm on abelian schemes

On p-adic interpolation of motivic Eisenstein classes

Polylogarithm for families of commutative group schemes

Rankin--Eisenstein classes and explicit reciprocity laws

Rankin--Eisenstein classes for modular forms

Higher analytic torsion, polylogarithms and norm compatible elements on abelian schemes

Topological polylogarithms and p-adic interpolation of L-values of totally real fields

Rankin-Selberg Euler systems and p-adic interpolation

Eisenstein classes, elliptic Soulé elements and the ℓ-adic elliptic polylogarithm

p-adic Beilinson conjecture for ordinary Hecke motives associated to imaginary quadratic fields

A cohomological Tamagawa number formula

Some complements to the Lazard isomorphism

On the equivariant and the non-equivariant main conjecture for imaginary quadratic fields

A note on polylogarithms on curves and abelian schemes

p-adic elliptic polylogarithm, p-adic Eisenstein series and Katz measure

A p-adic analogue of the Borel regulator and the Bloch-Kato exponential map

Degeneration of polylogarithms and special values of L-functions for totally real fields

On non-commutative twisting in etale and motivic cohomology

Equivariant Bloch-Kato conjecture and non-abelian Iwasawa Main Conjecture

Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters

$p$ -adic $L$ -functions for Hecke characters of totally imaginary fields

Algebraicity of critical Hecke $L$ -values

Another look at $p$ -adic Fourier-theory

Eisenstein-Kronecker classes, integrality of critical values of Hecke $L$ -functions and $p$ -adic interpolation

On $p$ -adic interpolation of motivic Eisenstein classes

Topological polylogarithms and $p$ -adic interpolation of $L$ -values of totally real fields

Eisenstein classes, elliptic Soulé elements and the $ℓ$ -adic elliptic polylogarithm

$p$ -adic Beilinson conjecture for ordinary Hecke motives associated to imaginary quadratic fields

A $p$ -adic analogue of the Borel regulator and the Bloch-Kato exponential map