
Ivan Rosas SotoÉcole Normale Supérieure de Lyon | ENS Lyon · UMR 5669 - Unité de Mathématiques Pures et Appliquées (UMPA)
Ivan Rosas Soto
PhD in Mathematics
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5
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Education
September 2020 - November 2023
September 2019 - August 2020
March 2013 - April 2019
Publications
Publications (5)
In the present article, we study the integral aspects of the Fourier transform of an abelian variety $A$ over a field $k$, using \'etale motivic cohomology, following the ideas and theory given by Moonen, Polishchuk and later by Beckman and de Gaay Fortman. We prove that there exists a PD-structure over the positive degree part of the \'etale Chow...
In the present article, we define an integral analogue of Chow-Künneth decomposition forétale motives. By using a suitable family of conservative functors, we are able to establish a decomposition of theétale motive of commutative group schemes over a base and we relate it to an integralétale Chow-Künneth decomposition of abelian varieties. For a p...
By using the triangulated category of \'etale motives over a field $k$, for a smooth projective variety $X$ over $k$, we define the group $\text{CH}^\text{\'et}_0(X)$ as an \'etale analogue of 0-cycles. We study the properties of $\text{CH}^\text{\'et}_0(X)$, giving a description about the birational invariance of such group. We define and present...
We define the category of \'etale Chow motives as the \'etale analogue of Grothendieck motives and proved that it embeds in $\text{DM}_{\text{\'et}}(k)$. This construction provides a characterization of the generalized Hodge conjecture in terms of an \'etale analogue of it. Finally we study the non-algebraic classes in the Atiyah-Hirzebruch, Benois...