TY - JOUR
T1 - Towards the Andre-Oort conjecture for mixed Shimura varieties
T2 - The Ax-Lindemann theorem and lower bounds for Galois orbits of special points
AU - Gao, Ziyang
N1 - Publisher Copyright:
© De Gruyter 2015.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
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U2 - 10.1515/crelle-2014-0127
DO - 10.1515/crelle-2014-0127
M3 - Article
AN - SCOPUS:84978366283
SN - 0075-4102
VL - 2015
SP - 85
EP - 146
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
ER -