Codimension 2
From Mathematics
(→Elementary algebraic K-Theory: K_0 and K_1) |
(→Elementary algebraic K-Theory: K_0 and K_1) |
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* The definition of <math>K_0(R)</math> for a ring <math>R</math> and <math>K_0(X)</math> for a variety <math>X</math>. | * The definition of <math>K_0(R)</math> for a ring <math>R</math> and <math>K_0(X)</math> for a variety <math>X</math>. | ||
* The Whitehead Lemma, 3.1<ref name="Mil71"/> and the definition of <math>K_1(R)</math> | * The Whitehead Lemma, 3.1<ref name="Mil71"/> and the definition of <math>K_1(R)</math> | ||
| − | * The localization exact sequence, if <math>R</math> is a | + | * The localization exact sequence, if <math>R</math> is a Dedekind ring, <math>K</math> its quotient field: |
| − | <math> K_1( | + | <math> \bigoplus_{\mathfrak{p}}K_1(R/\mathfrak{p}) \rightarrow K_1(R) \rightarrow K_1(K) \rightarrow \bigoplus_{\mathfrak{p}}K_1(R/\mathfrak{p}) K_0(R/\mathfrak{p}) \rightarrow K_0(R) \rightarrow K_0(K) \rightarrow 0 </math> |
References: §1-§5<ref name="Mil71"/>, | References: §1-§5<ref name="Mil71"/>, | ||
