Veranstaltung

Vortrag
K-theory of toric varieties
1.7.2013, 15:15 Uhr – 16:15 Uhr

This talk concerns the effect of dilations in the K-theory of monoidal algebras and schemes. We use multiplicative notation for monoids; if A is a monoid, and $a,b\in A$, then ab is their product. Any integer $n\ge 0$ defines a monoid homomorphism
A\to A, a\mapsto a^n
called the \emph{dilation} of ratio n. If $c=(n_1,n_2,\dots)$ is a sequence of integers $\ge 2$, we write $A^{1/c}$ for the result of formally adding an $n_1\cdots n_i$ root $a^{1/n_1\cdots n_i}$ for every $i\ge 1$ and every element $a\in A$. Joseph Gubeladze has conjectured that if R is a noetherian regular commutative ring, and A is torsion-free, cancellative and seminormal (all these conditions hold, for example, when A is toric), then the K-theory of the monoid algebra $R[A^{1/c}]$ is just the K-theory of R. That is, the inclusion $R\subset R[A^{1/c}]$ induces an isomorphism
K_*(R)=K_*(R[A^{1/c}])
Gubeladze proved his conjecture in the case when R contains a field of characteristic zero. In recent joint work with Haesemeyer, Walker and Weibel, we have proved that it also holds if R contains a field of positive characteristic. Thus the conjecture holds whenever R contains a field. In fact this is the affine case of a more general result on the effect of dilations on the K-theory of monoidal schemes. In the talk we intend to discuss all these results.

http://mate.dm.uba.ar/~gcorti/

Verknüpft mit:

• Guillermo Cortiñas