Ivan Rosas Soto

Ivan Rosas Soto
École Normale Supérieure de Lyon | ENS Lyon ·  UMR 5669 - Unité de Mathématiques Pures et Appliquées (UMPA)

PhD in Mathematics

About

5
Publications
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Citation
Education
September 2020 - November 2023
University of Burgundy
Field of study
  • Mathematics
September 2019 - August 2020
March 2013 - April 2019

Publications

Publications (5)
Article
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Preprint
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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...
Preprint
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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...
Preprint
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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...
Preprint
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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...