Algebraic K-theory of schemes and algebraic cycles
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 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.
Grothendieck, K groups of a scheme, Grothendieck, Categories de, Lambda-rings, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria K, Categories de, Grothendieck groups, Riemann-Roch theorems, Algebraic cycles, Classificació AMS::19 K-theory::19A Grothendieck groups and $K_0$
Grothendieck, K groups of a scheme, Grothendieck, Categories de, Lambda-rings, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria K, Categories de, Grothendieck groups, Riemann-Roch theorems, Algebraic cycles, Classificació AMS::19 K-theory::19A Grothendieck groups and $K_0$
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