16 citations · 43 across the 20 of their papers we have counts for
32 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…
The Grothendieck-Katz Conjecture for privileged local systems
Hélène Esnault, Michael Groechenig
We define study privileged local systems on a smooth quasi-projective complex variety with fixed quasi-unipotent monodromies around a boundary divisor. The notion is a generali…
Twisted Higgs bundles and coendoscopy
Michael Groechenig, Xuanyou Li, Dimitri Wyss +1
This short note is devoted to the study of -Higgs bundles twisted by a central gerbe. These objects arise naturally in the decomposition of the inertia stacks of -Higgs bundl…
Twisted points of quotient stacks, integration and BPS-invariants
Michael Groechenig, Dimitri Wyss, Paul Ziegler
We study -adic manifolds associated with twisted points of quotient stacks and their quotient spaces . We prove several structural res…
Cristallinity of rigid flat connections revisited
Hélène Esnault, Michael Groechenig
We generalise a theorem on the existence of Frobenius isocrystal and Fontaine-Laffaille module structures on rigid flat connections to the non-proper setting. The proof is based on…
Complex K-theory of moduli spaces of Higgs bundles
Michael Groechenig, Shiyu Shen
We establish an isomorphism of complex -theory of the moduli space of -Higgs bundles of degree and rank (in the sense of Hausel--Thaddeus)…
The de Rham stack and the variety of very good splittings of a curve
Mark Andrea A. de Cataldo, Michael Groechenig, Siqing Zhang
The stack of relative splittings of a special Azumaya algebra plays a key role in the Non-Abelian Hodge Theory for curves in positive characteristics. In this paper, we define and…
Rigid non-cohomologically rigid local systems
Johan de Jong, Hélène Esnault, Michael Groechenig
For any even natural number , we construct an irreducible rigid non-cohomologically rigid complex local system of rank on a smooth projective variety depending on .…
Classes in Zakharevich K-groups constructed from Quillen K-theory
Oliver Braunling, Michael Groechenig
We show that the K-groups K_{n}(O) for O the integers or an order in a CM field and n>0 appear as direct summands of the homotopy groups of various localisations of Zakharevich's K…
Canonical Heights on Shimura Varieties and the André-Oort Conjecture
Jonathan Pila, Ananth N. Shankar, Jacob Tsimerman +2
The main purpose of this work is to prove the André-Oort conjecture in full generality.
The standard realizations for the K-theory of varieties
Oliver Braunling, Michael Groechenig, Anubhav Nanavaty
The Grothendieck ring of varieties has well-known realization maps to, say, mixed Hodge structures or compactly supported -adic cohomology. Zakharevich and\ Campbell have dev…
Hypertoric Hitchin systems and Kirchhoff polynomials
Michael Groechenig, Michael McBreen
We define a formal algebraic analogue of hypertoric Hitchin systems, whose complex-analytic counterparts were defined by Hausel-Proudfoot. These are algebraic completely integrable…
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…
De Rham epsilon factors for flat connections on higher local fields
Michael Groechenig
This note is a companion to the author's "Higher de Rham epsilon factors". Using Grayson's binary complexes and the formalism of -Tate spaces we develop a formalism of graded ep…
Higher de Rham epsilon factors
Michael Groechenig
This article is devoted to the study of a higher-dimensional generalisation of de Rham epsilon lines. To a holonomic -module on a smooth variety and a generic tuple of $…
The -structure of the index map
Oliver Braunling, Michael Groechenig, Jesse Wolfson
Let be a local field with residue field . The classifying space of comes canonically equipped with a map to the delooping of the -theory space of . Passing t…
Cohomologically rigid local systems and integrality
Hélène Esnault, Michael Groechenig
We prove that the monodromy of an irreducible cohomologically complex rigid local system with finite determinant and quasi-unipotent local monodromies at infinity on a smooth quasi…
On the normally ordered tensor product and duality for Tate objects
Oliver Braunling, Michael Groechenig, Aron Heleodoro +1
This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal stru…
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…
Rigid connections and -isocrystals
Hélène Esnault, Michael Groechenig
An irreducible integrable connection on a smooth projective complex variety is called rigid if it gives rise to an isolated point of the corresponding moduli space…
Relative Tate Objects and Boundary Maps in the K-Theory of Coherent Sheaves
Oliver Braunling, Michael Groechenig, Jesse Wolfson
We investigate the properties of relative analogues of admissible Ind, Pro, and elementary Tate objects for pairs of exact categories, and give criteria for those categories to be…
Adelic Descent Theory
Michael Groechenig
A result of André Weil allows one to describe rank vector bundles on a smooth complete algebraic curve up to isomorphism via a double quotient of the set $\mathrm{GL}_n(\mathbb…
Geometric and analytic structures on the higher adèles
Oliver Braunling, Michael Groechenig, Jesse Wolfson
The adèles of a scheme have local components - these are topological higher local fields. The topology plays a large role since Yekutieli showed in 1992 that there can be an abunda…
Operator ideals in Tate objects
Oliver Braunling, Michael Groechenig, Jesse Wolfson
Tate's central extension originates from 1968 and has since found many applications to curves. In the 80s Beilinson found an n-dimensional generalization: cubically decomposed alge…