Cohomology of quasi-coherent sheaves over projective schemes

• Ano de defesa: 2021
• Autor(a) principal: Alvarez, Daniel Alberto Aguilar
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Cohomologia de feixes; Cohomologia local; Esquema projetivo; Feixe quasi-coherente; Local cohomology; Projective scheme; Quasi- coherent sheaf; Sheaf cohomology
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-11082021-113531/

The objective of this work is to present the reader with the study of some mathematical tools used in current problems of algebraic geometry, assuming only some knowledge in algebra and topology. We treat basic concepts and results in the theory of sheaves and schemes that we later use to understand the correspondence between local cohomology and sheaf cohomology of quasi-coherent sheaves over projective schemes. Then, with this background we are able to state some open problems that are related to the Hilbert polynomial and to the Castelonuovo-Mumford regularity of a coherent sheaf.