Regularization of relative holonomic D-modules

2022/10/30 by Fernandes, Teresa Monteiro
#14F10 #32C38 #35A27 #58J15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.16961

Abstract

Let X and S be complex analytic manifolds where S plays the role of a parameter space. Using the sheaf \DXS^∞ of relative differential operators of infinite order, we construct functorially the regular holonomic \DXS-module \shm_reg associated to a relative holonomic \DXS-module \shm, extending to the relative case classical theorems by Kashiwara-Kawai: denoting by \shm^∞ the tensor product of \shm by \DXS^∞ we explicit \shm^∞ in terms of the sheaf of holomorphic solutions of \shm and prove that \shm^∞ and \shm_reg^∞ are isomorphic.

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