collaborators

6 papers

math.AG2025

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…

math.AG2025

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…

math.AG2025

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…

math.AG2025

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…

math.AG2025

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…

math.AG2024

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…