Towards the Andre-Oort conjecture for mixed Shimura varieties: The Ax-Lindemann theorem and lower bounds for Galois orbits of special points

Ziyang Gao

Research output: Contribution to journalArticle

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Abstract

We prove in this paper the Ax-Lindemann-Weierstraß theorem for all mixed Shimura varieties and discuss the lower bounds for Galois orbits of special points of mixed Shimura varieties. In particular, we reprove a result of Silverberg [57] in a different approach. Then combining these results we prove the André-Oort conjecture unconditionally for any mixed Shimura variety whose pure part is a subvariety of An6 and under the Generalized Riemann Hypothesis for all mixed Shimura varieties of abelian type.

Original languageEnglish (US)
JournalJournal fur die Reine und Angewandte Mathematik
Volume2015
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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