19 citations · 73 across the 19 of their papers we have counts for
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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,…
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…
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…
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…
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.
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…