ERRATUM TO: CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES

Abstract

The proof of [1, Lemma 7.2] contains a gap: the equality $\omega _{\sharp } h_{0}(\Lambda _{\mathrm {ltr}}(\eta ,\mathrm {triv})) = \omega _{\sharp } h_{0}(\omega ^{*}\Lambda _{\mathrm {tr}}(\eta ))$ is false. Indeed one can check that for $X\in \mathbf {Sm}(k)$ proper, $$ \begin{align*} \operatorname{Hom}( \omega_{\sharp} h_{0}(\Lambda_{\mathrm{ltr}} (\eta_{X}, \mathrm{triv})), \mathbf{G}_{a}) \neq \operatorname{Hom}( \omega_{\sharp} h_{0} (\omega^{*} \Lambda_{{\mathrm{tr}}}( \eta_{X})) , \mathbf{G}_{a}), \end{align*} $$ as the left-hand side is $\mathbf {G}_{a}(\eta _{X})$ , whereas the right-hand side is $\mathbf {G}_{a}(X)$ . For now, we can give a proof only of a weaker version of [1, Proposition 7.3]: