Questions tagged [grothendieck-rings]

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11 votes
1 answer
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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 operations ...
darij grinberg's user avatar
29 votes
1 answer
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Is there a higher Grothendieck ring of varieties?

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 ...
Gring's user avatar
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8 votes
2 answers
770 views

Some questions about the map $K_0(\text{Var})\to K_0(\text{Mot})$

Let $k$ be a field. The naive Grothendieck ring of varieties $K_0(\text{Var})$ is generated by isomorphism classes of varieties over $k$ with the scissors relation $[X]=[X-Y]+[Y]$ for $Y$ a closed ...
peterx's user avatar
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3 votes
1 answer
425 views

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 $\...
THC's user avatar
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3 votes
1 answer
337 views

Field extensions in Grothendieck rings

Let $k$ be a field, and consider the Grothendieck ring of $k$-varieties, $K_0(V_k)$. Let $K/k$ and $K'/k$ be field extensions of $k$. We view $\mathrm{Spec}(K)$ and $\mathrm{Spec}(K')$ as $k$-schemes ...
THC's user avatar
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