Geodesic
Log $\mathscr{D}$-modules and index theorems
Forum of Mathematics, Sigma, Tome 9 (2021)

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We study log $\mathscr {D}$-modules on smooth log pairs and construct a comparison theorem of log de Rham complexes. The proof uses Sabbah’s generalized b-functions. As applications, we deduce a log index theorem and a Riemann-Roch type formula for perverse sheaves on smooth quasi-projective varieties. The log index theorem naturally generalizes the Dubson-Kashiwara index theorem on smooth projective varieties. 
@article{10_1017_fms_2020_62,
     author = {Lei Wu and Peng Zhou},
     title = {Log $\mathscr{D}$-modules and index theorems},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {9},
     year = {2021},
     doi = {10.1017/fms.2020.62},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.62/}
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Lei Wu; Peng Zhou. Log $\mathscr{D}$-modules and index theorems. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2020.62

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