47 citations · 77 across the 8 of their papers we have counts for
11 papers
-independence for K3-surfaces via -adic integration
Michael Groechenig, Dimitri Wyss, Paul Ziegler
This article provides a proof of a previously unknown case of Toda's -independence conjecture by reduction to non-archimedean local fields. Our strategy is based on a novel comp…
Normed Fiber Functors
Paul Ziegler
By Goldman-Iwahori, the Bruhat-Tits building of the general linear group over a local field can be described as the set of non-archimedean norms on $\e…
Tautological rings of Shimura varieties and cycle classes of Ekedahl-Oort strata
Torsten Wedhorn, Paul Ziegler
We define the tautological ring as the subring of the Chow ring of a Shimura variety generated by all Chern classes of all automorphic bundles. We explain its structure for the spe…
Geometric stabilisation via p-adic integration
Michael Groechenig, Dimitri Wyss, Paul Ziegler
In this article we give a new proof of Ngô's Geometric Stabilisation Theorem, which implies the Fundamental Lemma. This is a statement which relates the cohomology of Hitchin fibre…
Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration
Michael Groechenig, Dimitri Wyss, Paul Ziegler
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type and . More prec…
-kernels occurring in an isogeny class of -divisible groups
Paul Ziegler
We give a criterion which allows to determine, in terms of the combinatorics of the root system of the general linear group, which p-kernels occur in an isogeny class of p-divisibl…
Presentations for quaternionic -unit groups
Ted Chinburg, Holley Friedlander, Sean Howe +5
The purpose of this paper is to give presentations for projective -unit groups of the Hurwitz order in Hamilton's quaternions over the rational field . To our knowle…
Mordell-Lang in positive characteristic
Paul Ziegler
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture…
-zips with additional structure
Richard Pink, Torsten Wedhorn, Paul Ziegler
An -zip over a scheme over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtra…
Graded and Filtered Fiber Functors on Tannakian Categories
Paul Ziegler
We study fiber functors on Tannakian categories which are equipped with a grading or a filtration. Our goal is to give a comprehensive set of foundational results about such functo…
Algebraic zip data
Richard Pink, Torsten Wedhorn, Paul Ziegler
An algebraic zip datum is a tuple $\CZ := (G,P,Q,ϕ)$ consisting of a reductive group together with parabolic subgroups and and an isogeny . We…