20.500.12556/RUL-129595 Motivi in polenostavnost magistrsko delo Motives and semi-simplicity V nalogi obravnavamo teorijo (čistih) motivov, ki domnevno služi kot univerzalna kohomološka teorija v algebraični geometriji. Uvodoma se spomnimo osnovnih (Weilovih) kohomoloških teorij in motiviramo vpeljavo teorije motivov. V drugem poglavju pričnemo s ponovitvijo osnovne homološke algebre, kjer vpeljemo pojme kot so aditivna, psevdo-abelova in abelova kategorija. Tretje in četrto poglavje je namenjeno teoriji Tannaka kategorij, v četrtem poglavju jo spoznamo s stališča teorije skladov. V petem poglavju preko teorije algebraičnih ciklov vpeljemo pojem (čistega) motiva in dokažemo Jannsenov izrek o polenostavnosti kategorije numeričnih (čistih) motivov. In this Master's thesis we are concerned with the theory of (pure) motives, which is conjectured to serve as a universal or absolute cohomology theory in algebraic geometry. We begin with a reminder of the classical (Weil) cohomology theories for smooth projective varieties and give hints as to why we should believe that a theory of motives exists. In Chapter $2$, we recall some basic homological algebra, in particular we introduce the notions of additive, pseudo-abelian and abelian categories. We then discuss the theory of Tannakian categories in Chapters $3$ and $4$, where in Chapter 4 we consider the Tannakian theory from the viewpoint of stacks. In Chapter 5 we define the category of pure motives using the theory of algebraic cycles and prove Jannsen's theorem on the semi-simplicity of the category of numerical (pure) motives. algebraične varietete sheme kohomologija motivi algebraični cikli polenostavnost algebraic varieties schemes cohomology motives algebraic cycles semi-simplicity true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2021-09-05 08:15:07 2021-09-05 08:15:09 2024-05-29 14:00:03 0000-00-00 00:00:00 2021 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 119346 75185667 2749.pdf 2749.pdf 1 4B6E3B1CF3AAF8ABF122581C2927CA42 ef81e106e02be6fad9a167607ac770691b2f7ab42006cf1cd993a46cb610bb37 61c64825-0e10-11ec-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=146604 Fakulteta za matematiko in fiziko 0 0 0