The grothendieck-rings tag has no wiki summary.

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### On a property of the Grothendieck group of a smooth projective curve

Let $K$ be a complete DVR of characteristic $0$, $X$ a smooth projective curve over $K$. Denote by $K^0(X)$ the Grothendieck group of locally free sheaves on $X$ and by $\mbox{det}$ the natural group ...

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### Is there a higher Grothendieck ring?

Fix a field $k$. The Grothendieck ring $K_0(\mathrm{Var}_k)$ of varieties over $k$ is defined as the quotient of the free abelian group on isomorphism classes of algebraic varieties by the scissor ...

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### Virtual Lefschetz motive

Hi there,
I have a question which popped up while reading papers on motives.
Let $V_k$ be the category of (projective) k-varieties, and let $K_0(V_k)$ be the Grothendieck ring of $V_k$; then ...

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### Grothendieck ring of “varieties carrying a function”

Fix a base ring $R$, and consider pairs $(X,f)$ where $X$ is a scheme
of finite type over $R$ and $f:X\to R$ is an $R$-valued algebraic (not
constructible!) function on $X$.
I want to consider a ...

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### Higher K-theory of Orlik-Solomon algebras (and possible generalizations?)

This topic of this question is a bit outside my comfort zone, and I should say that my end goal is to really understand how much "graph theory" is captured by contraction-deletion relations. It seems ...

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### When are representation rings special lambda-rings? (variations of an old question)

Status: Questions 2 and 4 answered in the negative. Questions 1 and 3 ARE STILL UNANSWERED, despite previous claims.
On the third page of Wolfang K. Seiler's paper "lambda-rings and Adams ...