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Article: Ax-Schanuel for Shimura varieties
| Title | Ax-Schanuel for Shimura varieties |
|---|---|
| Authors | |
| Keywords | Ax-Schanuel Shimura variety |
| Issue Date | 2019 |
| Publisher | The Johns Hopkins University Press. The Journal's web site is located at http://www.press.jhu.edu/journals/annals_of_mathematics/index.html |
| Citation | Annals of Mathematics, 2019, v. 189 n. 3, p. 945-978 How to Cite? |
| Abstract | We prove the Ax-Schanuel theorem for a general (pure) Shimura variety. A basic version of the theorem concerns the transcendence of the uniformization map from a bounded Hermitian symmetric space to a Shimura variety. We then prove a version of the theorem with derivatives in the setting of jet spaces, and finally a version in the setting of differential fields.
Our method of proof builds on previous work, combined with a new approach that uses higher-order contact conditions to place varieties yielding intersections of excessive dimension in natural algebraic families. |
| Persistent Identifier | http://hdl.handle.net/10722/273893 |
| ISSN | 2023 Impact Factor: 5.7 2023 SCImago Journal Rankings: 7.154 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Mok, N | - |
| dc.contributor.author | Pila, J | - |
| dc.contributor.author | Tsimerman, J | - |
| dc.date.accessioned | 2019-08-18T14:50:46Z | - |
| dc.date.available | 2019-08-18T14:50:46Z | - |
| dc.date.issued | 2019 | - |
| dc.identifier.citation | Annals of Mathematics, 2019, v. 189 n. 3, p. 945-978 | - |
| dc.identifier.issn | 0003-486X | - |
| dc.identifier.uri | http://hdl.handle.net/10722/273893 | - |
| dc.description.abstract | We prove the Ax-Schanuel theorem for a general (pure) Shimura variety. A basic version of the theorem concerns the transcendence of the uniformization map from a bounded Hermitian symmetric space to a Shimura variety. We then prove a version of the theorem with derivatives in the setting of jet spaces, and finally a version in the setting of differential fields. Our method of proof builds on previous work, combined with a new approach that uses higher-order contact conditions to place varieties yielding intersections of excessive dimension in natural algebraic families. | - |
| dc.language | eng | - |
| dc.publisher | The Johns Hopkins University Press. The Journal's web site is located at http://www.press.jhu.edu/journals/annals_of_mathematics/index.html | - |
| dc.relation.ispartof | Annals of Mathematics | - |
| dc.rights | Annals of Mathematics. Copyright © The Johns Hopkins University Press. | - |
| dc.rights | Copyright © <year> The Johns Hopkins University Press. This article first appeared in TITLE, Volume <#>, Issue <#>, <Month>, <Year>, pages <#-#>. | - |
| dc.subject | Ax-Schanuel | - |
| dc.subject | Shimura variety | - |
| dc.title | Ax-Schanuel for Shimura varieties | - |
| dc.type | Article | - |
| dc.identifier.email | Mok, N: nmok@hku.hk | - |
| dc.identifier.authority | Mok, N=rp00763 | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.4007/annals.2019.189.3.7 | - |
| dc.identifier.scopus | eid_2-s2.0-85066923870 | - |
| dc.identifier.hkuros | 301638 | - |
| dc.identifier.volume | 189 | - |
| dc.identifier.issue | 3 | - |
| dc.identifier.spage | 945 | - |
| dc.identifier.epage | 978 | - |
| dc.identifier.isi | WOS:000467796700007 | - |
| dc.publisher.place | United States | - |
| dc.identifier.issnl | 0003-486X | - |