Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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  • Ziyang Gao

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OriginalspracheEnglisch
Aufsatznummere16
Seitenumfang65
FachzeitschriftForum of Mathematics, Sigma
Jahrgang7
PublikationsstatusVeröffentlicht - 27 Mai 2019

Abstract

We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. We study their bi-algebraic systems, formulate the Ax-Schanuel conjecture and explain its relation with the Ax logarithmique theorem and the Ax-Lindemann theorem which we shall prove. We also prove the whole Ax-Schanuel conjecture for the unipotent part. All these bi-algebraic and transcendental results generalize their counterparts for mixed Shimura varieties. In the end we briefly discuss about the Andre-Oort and Zilber-Pink type problems for enlarged mixed Shimura varieties.

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Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results. / Gao, Ziyang.
in: Forum of Mathematics, Sigma, Jahrgang 7, e16, 27.05.2019.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Gao Z. Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results. Forum of Mathematics, Sigma. 2019 Mai 27;7:e16. doi: 10.1017/fms.2019.10
Gao, Ziyang. / Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results. in: Forum of Mathematics, Sigma. 2019 ; Jahrgang 7.
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