19 citations · 99 across the 16 of their papers we have counts for
16 papers · 1 filter
A motivic proof of the finiteness of relative de Rham cohomology
Alberto Vezzani
We give a quick proof of the fact that the relative de Rham cohomogy groups of a smooth and proper map X/S between schemes over Q are vector bundles on the base, replacing Hodge-th…
A motivic approach to rational -adic cohomologies
Federico Binda, Alberto Vezzani
We survey over some recent applications of motivic homotopy theory in the definition and the study of -adic cohomology theories. In particular, we revisit the proof of the -a…
Ramified periods and field of definition
Giuseppe Ancona, Dragoş Frăţilă, Alberto Vezzani
Let be an extension of number fields that is ramified above . We give a new obstruction to the descent to of smooth projective varieties defined over . The obstruct…
Berthelot's conjecture via homotopy theory
Veronika Ertl, Alberto Vezzani
We use motivic methods to give a quick proof of Berthelot's conjecture stating that the push-forward map in rigid cohomology of the structural sheaf along a smooth and proper map h…
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…
On the p-adic weight-monodromy conjecture for complete intersections in toric varieties
Federico Binda, Hiroki Kato, Alberto Vezzani
We give a proof of the -adic weight monodromy conjecture for scheme-theoretic complete intersections in projective smooth toric varieties. The strategy is based on Scholze's pro…
The de Rham-Fargues-Fontaine cohomology
Arthur-César Le Bras, Alberto Vezzani
We show how to attach to any rigid analytic variety over a perfectoid space a rigid analytic motive over the Fargues-Fontaine curve functorially in and…
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…
Rigidity for rigid analytic motives
Federico Bambozzi, Alberto Vezzani
In this paper we prove the Rigidity Theorem for motives of rigid analytic varieties over a non-Archimedean valued field . We prove this theorem both for motives with transfers a…
Non-archimedean hyperbolicity and applications
Ariyan Javanpeykar, Alberto Vezzani
Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field of characteristic zero. We…
The Berkovich realization for rigid analytic motives
Alberto Vezzani
We prove that the functor associating to a rigid analytic variety the singular complex of the underlying Berkovich topological space is motivic, and defines the maximal Artin quoti…
Rigid cohomology via the tilting equivalence
Alberto Vezzani
We define a de Rham cohomology theory for analytic varieties over a valued field of equal characteristic with coefficients in a chosen untilt of the perfection of $K^…
The Monsky-Washnitzer and the overconvergent realizations
Alberto Vezzani
We construct the dagger realization functor for analytic motives over non-archimedean fields of mixed characteristic, as well as the Monsky-Washnitzer realization functor for algeb…
Effective motives with and without transfers in characteristic
Alberto Vezzani
We prove the equivalence between the category of effective motives of rigid analytic varieties over a perfect complete non-archimedean fie…
A motivic version of the theorem of Fontaine and Wintenberger
Alberto Vezzani
We prove the equivalence between the categories of motives of rigid analytic varieties over a perfectoid field of mixed characteristic and over the associated (tilted) perfecto…
Deitmar's versus Toen-Vaquie's schemes over F_1
Alberto Vezzani
We show the equivalence between Deitmar's and Toen-Vaquie's notions of schemes over F_1 (the 'field with one element'), establishing a symmetry with the classical case of schemes,…