Algebraic K-theory of schemes and algebraic cycles
In this thesis, we introduce the K groups of a scheme. One of the motivations for the definition of the K groups is to prove a generalized version of the Riemann-Roch Theorem. We introduce the K groups of a scheme and several constructions on them. We descrive geometric notions such as intersections...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/87182 |
| Acceso en línea: | https://hdl.handle.net/2117/87182 |
| Access Level: | acceso abierto |
| Palabra clave: | Grothendieck groups K groups of a scheme Algebraic cycles Lambda-rings Riemann-Roch theorems Grothendieck, Categories de Classificació AMS::19 K-theory::19A Grothendieck groups and $K_0$ Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria K |
| Sumario: | In this thesis, we introduce the K groups of a scheme. One of the motivations for the definition of the K groups is to prove a generalized version of the Riemann-Roch Theorem. We introduce the K groups of a scheme and several constructions on them. We descrive geometric notions such as intersections and self-intersections in terms of the K groups, and later we use these notions to construct filtrations, the topological filtration on the G group and the gamma filtration on the K group, to eventually construct a replacement for the cohomology, which can be used to define the Chern character and the Todd class, the necessary ingredients to state the Grothendieck-Riemann-Roch Theorem. |
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