7 papers
Pro-étale motives and solid rigidity
Raphaël Ruimy, Swann Tubach, Sebastian Wolf
We introduce coefficient systems of pro-étale motives and pro-étale motivic spectra with coefficients in any condensed ring spectrum and show that they afford the six operations. O…
The weight filtration on real singular homology is motivic
Raphaël Ruimy
We give an alternative construction of Totaro's weight filtration on singular homology of the real points of a real algebraic variety. Our construction shows that this filtration c…
Deligne 1-motives with torsion and étale motives
Raphaël Ruimy
We construct the motivic t-structure on 1-motives with integral coefficients over a scheme of characteristic zero or a Dedekind scheme. When we invert the residue characteristic ex…
Integral Artin motives II: Perverse motives and Artin Vanishing Theorem
Raphaël Ruimy
In this text, we are mainly interested in the existence of the perverse motivic t-structures on the category of Artin étale motives with integral coefficients. We construct the per…
Nori motives (and mixed Hodge modules) with integral coefficients
Raphaël Ruimy, Swann Tubach
We construct abelian categories of integral Nori motivic sheaves over a scheme of characteristic zero. The first step is to study the presentable derived category of Nori motives o…
Étale motives of geometric origin
Raphaël Ruimy, Swann Tubach
Over qcqs finite-dimensional schemes, we prove that étale motives of geometric origin can be characterised by a constructibility property which is purely categorical, giving a full…
Integral Artin motives I: Smooth objects and the ordinary t-structure
Raphaël Ruimy
We link smooth Artin motives to étale local systems and Artin representations. We then construct the ordinary motivic t-structure on Artin motives with integral coefficients and sh…