My research covers algebraic geometry, theory of motives, Hodge theory, algebraic cycles and motivic cohomology, with a specialization in étale motivic cohomology and the Chow-Künneth decomposition. In my Ph.D. Thesis I achieve to obtain the decomposition of the étale motive of a commutative group scheme over a base with integral coefficients and also the existence of integral projectors in the category of étale motives as the result with rational coefficients proved by Murre. In addition, I obtained an equivalent statement of the generalized Hodge conjecture in terms of étale motivic cohomology.
I. Rosas-Soto, Etale degree map and 0-cycles. In: Journal of Algebra, Volume 665, 1 March 2025, Pages 384-414.
P. Montero, I. Rosas-Soto, Algebraic cycles of some Fano varieties with Hodge structure of level one. (2025). arXiv version
I. Rosas-Soto, Integral Fourier transform of étale motivic cohomology. (2024). arXiv version
I. Rosas-Soto, Chow-Künneth decomposition for étale motives. (2024). arXiv version
I. Rosas-Soto, Hodge structures through an étale motivic point of view. (2022). arXiv version
Higher Brauer groups and actions on zero cycles.
Decomposition of integral étale motives and Deligne-Mumford stacks.
Cohomologie étale. (Notes)
Suite exponentielle pour la cohomologie réelle de Deligne. (Notes)
The Gersten conjecture for Rost complexes. (Notes)
Chow groups with coefficients. (Notes)
Computations mixed Hodge structures. (Notes)
Mathematical engineering thesis: "Problemas de Control óptimo Totalmente Convexos de Ecuaciones Diferenciales Parciales" (pdf)
Memoir Undergraduate in Mathematics: "Curvas Algebraicas y Resolución de Singularidades Monomiales" (pdf)