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

Abstract:
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..