La geometr\'ia de los Monoides
Abstract
In this article we present the basis of Monoid Theory from a categorical point of view, emphasizing the analogies and differences between the theory of modules over commutative rings. We present the generalization of afine schemes and afine monoidal schemes. We study the relationship between the former two with opic varieties and we set up the basis for the study of Fontaine-Kato-Illusie's Logaritmic Geometry, widely used in Arithmetic Geometry. En este art\'iculo presentamos las bases de la teor\'ia de monoides desde el punto de vista categ\'orico, haciendo \'enfasis en las analog\'ias y diferencias entre la teor\'ia de m\'odulos sobre anillos conmutativos. Se presenta la generalizaci\'on de esquema af\'in a esquema af\'in monoidal; estudiamos la relaci\'on que \'estos tienen con las variedades t\'oricas y sentamos las bases para el estudio de la Geometr\'ia Logar\'itmica de Fontaine-Kato-Illusie~\cite{kato1989logarithmic}, ampliamente usada en Geometr\'ia Aritm\'etica.
Keywords
Cite
@article{arxiv.2209.02110,
title = {La geometr\'ia de los Monoides},
author = {J. Rogelio Perez-Buendia and Ernesto Antonio Reyes-Ramirez},
journal= {arXiv preprint arXiv:2209.02110},
year = {2022}
}
Comments
72 pages, in Spanish language