论文标题
模量的动机，iii：动机类别
Motives with modulus, III: The categories of motives
论文作者
论文摘要
我们通过模量$ \ mathbf {mdm} _ {\ mathrm {gm}}}^{\ mathrm {eff}} $构建和研究动机的三角形类别$ \ mathbf {dm} _ {\ mathrm {gm}}}^{\ mathrm {eff}}} $以包含非亲子不变现象的方式。以类似的方式与$ \ MathBf {dm} _ {\ Mathrm {gm}}}^{\ Mathrm {eff}} $由平滑的$ k $ -Varieties，$ \ Mathbf {Mdm} _ {\ Mathrm {\ Mathrm} $ {模量对，在这项工作的第一部分中引入。对于这样的模量对，我们将其动机与$ \ mathbf {mdm} _ {\ mathrm {gm}}}}^{\ Mathrm {eff}} $相关联。在某些情况下，$ \ mathrm {hom} $ group中的$ \ mathbf {mdm} _ {\ mathrm {gm}}}^{\ mathrm {eff}} $在两个模量对的动机之间可以用布洛克更高的chow组来描述两个模量对的动机之间。
We construct and study a triangulated category of motives with modulus $\mathbf{MDM}_{\mathrm{gm}}^{\mathrm{eff}}$ over a field $k$ that extends Voevodsky's category $\mathbf{DM}_{\mathrm{gm}}^{\mathrm{eff}}$ in such a way as to encompass non-homotopy invariant phenomena. In a similar way as $\mathbf{DM}_{\mathrm{gm}}^{\mathrm{eff}}$ is constructed out of smooth $k$-varieties, $\mathbf{MDM}_{\mathrm{gm}}^{\mathrm{eff}}$ is constructed out of proper modulus pairs, introduced in Part I of this work. To such a modulus pair we associate its motive in $\mathbf{MDM}_{\mathrm{gm}}^{\mathrm{eff}}$. In some cases the $\mathrm{Hom}$ group in $\mathbf{MDM}_{\mathrm{gm}}^{\mathrm{eff}}$ between the motives of two modulus pairs can be described in terms of Bloch's higher Chow groups.
