论文标题
相对动机的派生类别上的Hodge实现函数
The Hodge realization functor on the derived category of relative motives
论文作者
论文摘要
对于复杂的代数品种$ s $，我们提供了一个hodge实现函数$ \ MATHCAL F_S^{HDG} $，从构造动机的派生类别$ da_c（s）$ da_c（s）$ da_c（s）$ d（s）$ d（mhm（s））$ d（mhm（s））$ bach $ s $ s $ s $ s $。此外，对于$ f：t \至s $，复杂的准标记代数品种的形态，$ \ nathcal f _ { - }^{hdg} $与四个操作$ f^*$，$ f^*$，$ f _*$，$ f _*$，$ f _！$，$ f _！$，$ f^！ functor a morphism of 2-functor wich for a given $S$ sends $DA_c(S)$ to $D(MHM(S)$, moreover $\mathcal F_S^{Hdg}$ commutes with tensor product. We also give an algebraic and analytic Gauss-Manin realization functor from which we obtain a base change theorem for algebraic De Rham cohomology and for all smooth形态是代数de rham的共同体学与分析性DE RHAM的共同体之间的Grothendieck比较定理的房地产。
We give, for a complex algebraic variety $S$, a Hodge realization functor $\mathcal F_S^{Hdg}$ from the derived category of constructible motives $DA_c(S)$ to the derived category $D(MHM(S))$ of algebraic mixed Hodge modules over $S$. Moreover, for $f:T\to S$ a morphism of complex quasi-projective algebraic varieties, $\mathcal F_{-}^{Hdg}$ commutes with the four operation $f^*$,$f_*$,$f_!$,$f^!$ on $DA_c(-)$ and $D(MHM(-))$, making the Hodge realization functor a morphism of 2-functor wich for a given $S$ sends $DA_c(S)$ to $D(MHM(S)$, moreover $\mathcal F_S^{Hdg}$ commutes with tensor product. We also give an algebraic and analytic Gauss-Manin realization functor from which we obtain a base change theorem for algebraic De Rham cohomology and for all smooth morphisms a realtive version of the comparaison theorem of Grothendieck between the algebaric De Rham cohomology and the analytic De Rham cohomology.
