All Questions

In "The universal Euler characteristic for varieties of characteristic zero", Bittner shows that over a field $k$ of characteristic zero, the Grothendieck ring $K_{0}(Var_{k})$ of varieties ...

Here's a problem that may ultimately require just simple algebraic-geometry skills to be solved, or perhaps it's very deep and will never be solved at all. From the comments, some literature and my ...

Are there known examples of a non-multiplicative Euler-Poincaré characteristic on varieties? Let $\mathbf{Var}/k$ be the category of varieties over a filed $k$, i.e. the category of reduced separated ...

By a generalized Euler characteristic $\chi$, I mean an isomorphism invariant $\chi(V)$ inside some abelian group $A$, defined for every varietiy $V$ over a field $k$, with the property that, for all ...

Let $K_0(Var_k)$ be the abelian group generated by the isomorphism classes of varieties over the field $k$ with the relations $$[X]=[U]+[X\setminus U]$$ for every variety $X$ and open subvariety $U$. ...