{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:50:23Z","timestamp":1762955423055,"version":"3.45.0"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Publ. Res. Inst. Math. Sci."],"published-print":{"date-parts":[[2024,11,7]]},"abstract":"<jats:p>\n                    Let\n                    <jats:inline-formula>\n                      <jats:tex-math>X<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:tex-math>S<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    be complex analytic manifolds where\n                    <jats:inline-formula>\n                      <jats:tex-math>S<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    plays the role of a parameter space. Using the sheaf\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{D}_{X\\times S\/S}^{\\infty}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    of relative differential operators of infinite order, we construct functorially the regular holonomic\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{D}_{X\\times S\/S}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -module\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{M}_{{\\mathrm{reg}}}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    associated to a relative holonomic\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{D}_{X\\times S\/S}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -module\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{M}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , extending to the relative case classical theorems by Kashiwara\u2013Kawai: denoting by\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{M}^{\\infty}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    the tensor product of\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{M}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    by\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{D}_{X\\times S\/S}^{\\infty}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    we make\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{M}^{\\infty}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    explicit in terms of the sheaf of holomorphic solutions of\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{M}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . As a consequence of the relative Riemann\u2013Hilbert correspondence we conclude that\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{M}^{\\infty}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathcal{M}_{{\\mathrm{reg}}}^{\\infty}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    are isomorphic.\n                  <\/jats:p>","DOI":"10.4171\/prims\/60-4-6","type":"journal-article","created":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T06:53:54Z","timestamp":1730962434000},"page":"815-829","source":"Crossref","is-referenced-by-count":0,"title":["Regularization of Relative Holonomic $\\mathcal{D}$-Modules"],"prefix":"10.4171","volume":"60","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4014-9868","authenticated-orcid":false,"given":"Teresa","family":"Monteiro Fernandes","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01c27hj86","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade de Lisboa, Lisboa, Portugal"}]}],"member":"2673","container-title":["Publications of the Research Institute for Mathematical Sciences"],"original-title":[],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:39:45Z","timestamp":1762954785000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/prims\/60-4-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,7]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.4171\/prims\/60-4-6","relation":{},"ISSN":["0034-5318","1663-4926"],"issn-type":[{"type":"print","value":"0034-5318"},{"type":"electronic","value":"1663-4926"}],"subject":[],"published":{"date-parts":[[2024,11,7]]}}}