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Some basic facts about algebraic $K$-theory

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#abstract-algebra #ring-theory #category-theory #algebraic-k-theory
104
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$M$ and $N$ equal in $K_0$ $\Rightarrow$ $\exists P$ such that $M\oplus P\cong N\oplus P$

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#abstract-algebra #projective-module #algebraic-k-theory
78
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Some properties of $K_i(\mathcal C)$

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#general-topology #algebraic-geometry #category-theory #algebraic-k-theory
75
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Example of Waldhausen category with quotient maps not closed under composition

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#category-theory #homotopy-theory #topological-k-theory #algebraic-k-theory
218
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Showing an isomorphism of $R[G]$-modules using the regular representation

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#modules #representation-theory #noncommutative-algebra #group-rings #algebraic-k-theory
62
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Is there an 'easy' way to calculate $K_0(\mathbb{Z}[C_p])$?

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#number-theory #group-rings #algebraic-k-theory #ideal-class-group
56
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If $P$ is a fg projective $\mathbb{Z}[G]$-module, what is $P\otimes\mathbb{R}$?

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#abstract-algebra #modules #algebraic-k-theory #projective-module #group-rings
54
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The multiplication '$*$' of the ring $W(K)=1+tK[[t]]$ in C.Weibel's 'The K-book'

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#abstract-algebra #formal-power-series #algebraic-k-theory #lambda-rings
48
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The definition of (special) $\lambda$-rings by using the ring $W(K)$ of big Witt vectors.

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#abstract-algebra #algebraic-k-theory #lambda-rings
43
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When is the representation ring of neutral component of reductive group flat?

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#algebraic-geometry #algebraic-groups #algebraic-k-theory
186
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Pushforward of the Segre embedding in K-theory

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#algebraic-geometry #projective-space #coherent-sheaves #projective-schemes #algebraic-k-theory
79
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What is the Grothendieck (K_0) group of the ring of Laurent polynomials?

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#ring-theory #laurent-series #projective-module #algebraic-k-theory #grothendieck-construction
42
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stable range of stably free modules

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#solution-verification #projective-module #artinian #algebraic-k-theory #semi-simple-rings
117
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Give an example of a commutative ring with unity $R$, such that $K_0(R) \ncong K_0(R[t])$

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#commutative-algebra #algebraic-k-theory #picard-group
41
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On the norm map in Milnor K-theory for $K_2$

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#number-theory #algebraic-number-theory #algebraic-k-theory

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