Geodesic
Homological Planes in the Grothendieck Ring of Varieties
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 356-362

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we identify the classes of $\text{Q}$ -homological planes in the Grothendieck group of complex varieties ${{K}_{0}}\left( \text{Va}{{\text{r}}_{\text{C}}} \right)$ . Precisely, we prove that a connected, smooth, affine, complex, algebraic surface $X$ is a $\text{Q}$ -homological plane if and only if $\left[ X \right]\,=\,\left[ \text{A}_{\text{C}}^{2} \right]$ in the ring ${{K}_{0}}\left( \text{Va}{{\text{r}}_{\text{C}}} \right)$ and $\text{Pic}{{\left( X \right)}_{\text{Q}}}\,:=\,\text{Pic}\left( X \right)\,{{\otimes }_{\text{Z}}}\,\text{Q}\,\text{=}\,\text{0}$ .
DOI : 10.4153/CMB-2014-045-6
Mots-clés : 14E05, 14R10, motivic nearby cycles, motivic Milnor fiber, nearby motives 
Sebag, Julien. Homological Planes in the Grothendieck Ring of Varieties. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 356-362. doi: 10.4153/CMB-2014-045-6
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