Algebraic K-theory is a tool from homological algebra that defines a sequence of functors from rings to abelian groups. It has many applications in algebraic geometry. See also (topological-k-theory).
Questions tagged [algebraic-k-theory]
212 questions
8
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higher K-theory of complex numbers
What is known about the higher algebraic K-theory of the complex numbers $\mathbb{C}$?
It's obvious that $K_0(\mathbb{C}) = \mathbb{Z}$. According to Wikipedia, it seems like we should have $K_1(\mathbb{C}) = \mathbb{C}^\times$. It seems like one…
user148177
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Milnor $K_2$ of an inverse limit is inverse limit of Milnor $K_2$'s?
Let $\{A_n\}$ be an inverse system of rings and $\hat{A}$ be the inverse limit of this system. Let $K_2(R)$ denote Milnor $K_2$ (I will assume that the case I am interested in the Milnor $K_2$ is isomorphic to algebraic $K_2$ of Quillen).
Question:…
user9509
- 71
4
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1 answer
Meaning of K in Algebraic K theory
I am reading algebraic K-theory but I have doubt not in the subject but in the name. I want to ask what K stands in the word Algebraic K-theory as well as in Topological K-theory.
Sunny
- 1,359
2
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1 answer
Question on K-theory
If $R$ is a ring with 1 which satisfies $R^r=R^s$ for some $r\neq s$.
Are there any explicit calculation of $K_0(R)$ for such $R$?
I want to know such examples because I think that such $R$ may not have $\mathbb{Z}$-summands.
user8484
- 801
2
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0 answers
Eilenberg-MacLane rings in algebraic K theory?
Given any abelian group $G$ and a natural number $n$, is there always a ring (unital) whose algebraic K-groups are $K_i(R)=0, i\neq n$ and $K_n(R)=G$?
1
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reference request for finiteness theorem for $K_2$
Is there an algebraic proof of the finiteness theorem for $K_2$ of number fields available?
The Garland's proof (1971) heavily relies on transcendental methods.
Dmitry K
- 406
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1
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1 answer
$K$-theory of formal power series.
I was wondering whether there is a calculation of algebraic $K$-groups of the formal power series $\mathbb{F}_p[[x]]$?
user127776
- 1,364
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1 answer
Basic question on $K$-theory
Let $h\colon A\to A'$ be a ring homomorphism between $A,A'$ which are commutative rings with $1$.
Let $P,Q$ be $A$-modules. Then, are there any gaps in my following…
user8484
- 801
0
votes
2 answers
Motivation of $G_0$ group
I want to know the motivation why we want to modulo the subgroup related to the exact sequences.
6666
- 3,687