Log $\mathscr{D}$-modules and index theorems
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 varieti...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2021-01-01
|
| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509420000626/type/journal_article |
| _version_ | 1811156200158396416 |
|---|---|
| author | Lei Wu Peng Zhou |
| author_facet | Lei Wu Peng Zhou |
| author_sort | Lei Wu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T04:47:31Z |
| format | Article |
| id | doaj.art-c65466a9b7b441f7978da060d0b899a8 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:31Z |
| publishDate | 2021-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-c65466a9b7b441f7978da060d0b899a82023-03-09T12:34:52ZengCambridge University PressForum of Mathematics, Sigma2050-50942021-01-01910.1017/fms.2020.62Log $\mathscr{D}$-modules and index theoremsLei Wu0Peng Zhou1Department of Mathematics, University of Utah, 155 South 1400 E, Salt Lake City, UT 84112, USA; E-mail: .Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, CA 94720-3840, USA; E-mail: .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.https://www.cambridge.org/core/product/identifier/S2050509420000626/type/journal_article14F1032S4032S6014C1714C40 |
| spellingShingle | Lei Wu Peng Zhou Log $\mathscr{D}$-modules and index theorems Forum of Mathematics, Sigma 14F10 32S40 32S60 14C17 14C40 |
| title | Log $\mathscr{D}$-modules and index theorems |
| title_full | Log $\mathscr{D}$-modules and index theorems |
| title_fullStr | Log $\mathscr{D}$-modules and index theorems |
| title_full_unstemmed | Log $\mathscr{D}$-modules and index theorems |
| title_short | Log $\mathscr{D}$-modules and index theorems |
| title_sort | log mathscr d modules and index theorems |
| topic | 14F10 32S40 32S60 14C17 14C40 |
| url | https://www.cambridge.org/core/product/identifier/S2050509420000626/type/journal_article |
| work_keys_str_mv | AT leiwu logmathscrdmodulesandindextheorems AT pengzhou logmathscrdmodulesandindextheorems |