24 citations · 89 across the 6 of their papers we have counts for
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Weil cohomology theories and their motivic Hopf algebroids
Joseph Ayoub
In this paper we discuss a general notion of Weil cohomology theories, both in algebraic geometry and in rigid analytic geometry. We allow our Weil cohomology theories to have coef…
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…
Nori 1-motives
J. Ayoub, L. Barbieri-Viale
Let EHM be Nori's category of effective homological mixed motives. In this paper, we consider the thick abelian subcategory EHM_1 generated by the i-th relative homology of pairs o…
Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety
Joseph Ayoub, Steven Zucker
We introduce the notion of Artin motives and cohomological motives over a scheme X. Given a cohomological motive M over X, we construct its punctual weight zero part as…
1-motivic sheaves and the Albanese functor
J. Ayoub, L. Barbieri-Viale
We introduce n-generated sheaves and n-motivic sheaves, describing completely for n = 0, 1 and proposing a conjecture for n > 1. We then obtain functors Lπ_0 and LAlb on DM_{eff}(k…