与光滑态射相关的D-模的调和解的微支撑
Microsupport of tempered solutions of D-Modules associated to smooth morphisms
摘要：
设$f:X\to Y$是复解析流形的光滑态射，$F$是$Y$上的$\mathbb{R}$ -可构造复形.设$\cal{M}$是一个相干的$\shd_X$ -模块。我们证明了$\shm$在回火全纯函数$t \shh \text{om} (f^{-1} F, \sho_X)$中的解复形的微支集包含在与$f$相关的$\cal{M}$的1-特征簇中，并且在回火微函数$tμhom(f^{-1}F, \sho_X)$中的解复形的微支集包含在沿$T^*Y\times_Y X$的$\shm$的微局部化的1-微特征簇中。这特别适用于复杂的解决方案的$\shm$在层的分布全纯的纤维中的任意光滑态射。
英文摘要：
Let $f:X\to Y$ be a smooth morphism of complex analytic manifolds and let $F$ be an $\mathbb{R}$-constructible complex on $Y$. Let $\cal{M}$ be a coherent $\shd_X$-module. We prove that the microsupport of the solution complex of $\shm$ in the tempered holomorphic functions $t \shh \text{om} (f^{-1} F, \sho_X)$, is contained in the 1-characteristic variety of $\cal{M}$ associated to $f$, and that the microsupport of the solution complex in the tempered microfunctions $tμhom(f^{-1}F, \sho_X)$ is contained in the 1-microcharacteristic variety of the microlocalized of $\shm$ along $T^*Y\times_Y X$. This applies in particular to the complex of solutions of $\shm$ in the sheaf of distributions holomorphic in the fibers of an arbitrary smooth morphism.
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