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arXiv · 2209.02110

La geometr\'ia de los monoides

J. Rogelio Pérez-Buendía·Ernesto Antonio Reyes-Ramírez
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Abstract

In this article we present the basis of Monoid Theory from a categorical point of view, emphasizing the analogies and differences with the theory of modules over commutative rings. We present the generalization of affine schemes to affine monoidal schemes. We study the relationship between the latter and toric varieties, and we set up the basis for the study of Fontaine-Kato-Illusie's Logarithmic 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 con 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, ampliamente usada en Geometr\'ia Aritm\'etica.

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J. Rogelio Pérez-Buendía, Ernesto Antonio Reyes-Ramírez. 2022-09-05. La geometr\'ia de los monoides. https://arxiv.org/abs/2209.02110

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