arXiv subjects

Ivan Rosas-Soto

Publications and source records attributed to Ivan Rosas-Soto.

3 recordsLinked to original sources

arXiv2025

Étale degree map and 0-cycles

By using the triangulated category of étale motives over a field $k$, for a smooth projective variety $X$ over $k$, we define the group $\text{CH}^\text{ét}_0(X)$ as an étale analogue of 0-cycles. We study the properties of $\text{CH}^\text{ét}_0(X)$, giving a description about the birational invariance of such group. We define and present the étale degree map by using Gysin morphisms in étale motivic cohomology and the étale index as an analogue to the classical case. We give examples of smooth projective varieties over a field $k$ without zero cycles of degree one but with étale zero cycles of degree one, however, this property is not always true as we present examples where the étale degree map is not surjective.

math.AG↗

arXiv2024

Fourier transform for étale motivic cohomology

In the present article, we study the integral aspects of the Fourier transform of an abelian variety $A$ over a field $k$, using étale 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 étale Chow ring $\text{CH}^{\text{ét}}_{>0}(A)$ with respect to the Pontryagin product.

math.AG↗

arXiv2024

Chow Künneth decomposition for étale motives

In the present article we define an integral analogue of Chow-Künneth decomposition for étale motives. By using families of conservative functors we are able to establish a decomposition of the étale motive of commutative group schemes over a base and we relate to an integral étale Chow-Künneth decomposition of abelian varieties. For a projective variety $X$ of dimension $d$ over an algebraically closed field, we construct integral sub-motives $h^1_{\text{ét}}(X)$ and $h^{2d-1}_{\text{ét}}(X)$ of the motive $h_{\text{ét}}(X)$.

math.AG↗