Plática dada por Paulo Lima-Filho (Texas A&M University) en el Segundo Congreso Nacional de Geometría Algebraica el lunes 26 de febrero del 2018 Casa Matemática Oaxaca, en Oaxaca de Juárez, México
Using Suslin's generic equidimensionality results, we provide an elementary and direct proof of the isomorphism between the cubical and simplicial versions of Bloch's higher Chow groups for equidimensional quasi-projective schemes of finite type over a field
k. We show that in the derived category, the cubical and simplicial complexes are lax monoidal functors and give an isomorphism that stems from a natural transformation of lax monoidal functors. In particular, in the case of regular schemes we have an isomorphism of bigraded rings. The same constructions also yield a corresponding isomorphism between the singular and cubical homology in the category of topological spaces..