19 citations · 73 across the 19 of their papers we have counts for
19 papers
Permutation, stabilization and decomposition
Paul Balmer, Martin Gallauer
Informed by our understanding of the tt-geometry of permutation modules, we investigate the proper definition of the `stable permutation category' of a finite group. Then we prove…
Periods in equivariant and motivic contexts
Martin Gallauer
We define the period as a multiplicative characteristic of stably symmetric monoidal -categories, develop its basic properties, and study many examples, with a focus on `or…
Patch-density in tensor-triangular geometry
Paul Balmer, Martin Gallauer
The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology. We prove that patch-dense…
The spectrum of Artin motives
Paul Balmer, Martin Gallauer
We analyze the tt-geometry of derived Artin motives, via modular representation theory of profinite groups. To illustrate our methods, we discuss Artin motives over a finite field,…
The geometry of permutation modules
Paul Balmer, Martin Gallauer
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We des…
Motivic monodromy and p-adic cohomology theories
Federico Binda, Martin Gallauer, Alberto Vezzani
We build a unified framework for the study of monodromy operators and weight filtrations of cohomology theories for varieties over a local field. As an application, we give a strea…
Exponentiation of coefficient systems and exponential motives
Martin Gallauer, Simon Pepin Lehalleur
We construct new six-functor formalisms capturing cohomological invariants of varieties with potentials. Starting from any six-functor formalism , encoded as a coefficient syste…
The tt-geometry of permutation modules. Part I: Stratification
Paul Balmer, Martin Gallauer
We consider the derived category of permutation modules over a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We de…
An introduction to six-functor formalisms
Martin Gallauer
These are notes for a mini-course given at the summer school and conference "The Six-Functor Formalism and Motivic Homotopy Theory" in Milan 9/2021. They provide an introduction to…
Permutation modules, Mackey functors, and Artin motives
Paul Balmer, Martin Gallauer
We explain in detail the connections between the three concepts in the title, and we discuss how the `big' derived category of permutation modules introduced in arXiv:2009.14093 fi…
Supports for constructible systems
Martin Gallauer
We develop a `universal' support theory for derived categories of constructible (analytic or étale) sheaves, holonomic D-modules, mixed Hodge modules and others. As applications we…
The six-functor formalism for rigid analytic motives
Joseph Ayoub, Martin Gallauer, Alberto Vezzani
We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base ch…
Permutation modules and cohomological singularity
Paul Balmer, Martin Gallauer
We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and take…
Finite permutation resolutions
Paul Balmer, Martin Gallauer
We prove that every finite dimensional representation of a finite group over a field of characteristic p admits a finite resolution by p-permutation modules. The proof involves a r…
The universal six-functor formalism
Brad Drew, Martin Gallauer
We prove that Morel-Voevodsky's stable -homotopy theory affords the universal coefficient system, giving rise to Grothendieck's six operations.
Statistical mechanics of kinks on a gliding screw dislocation
M. Boleininger, M. Gallauer, S. L. Dudarev +3
The ability of a body-centered cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility ex…
A note on Tannakian categories and mixed motives
Martin Gallauer
We explain why every non-trivial exact tensor functor on the triangulated category of mixed motives over a field F has zero kernel, if one assumes "all" motivic conjectures. In oth…
Three real Artin-Tate motives
Paul Balmer, Martin Gallauer
We analyze the spectrum of the tensor-triangulated category of Artin-Tate motives over the base field R of real numbers, with integral coefficients. Away from 2, we obtain the same…
tt-geometry of Tate motives over algebraically closed fields
Martin Gallauer
We study Tate motives with integral coefficients through the lens of tensor triangular geometry. For some base fields, including the field of algebraic numbers and the algebraic cl…