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

Ziyang Gao

doi:10.1017/fms.2019.10

Details

Original language	English
Article number	e16
Number of pages	65
Journal	Forum of Mathematics, Sigma
Volume	7
Publication status	Published - 27 May 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.

Keywords

math.AG, math.NT, 11G18, 11J81, 14G35, 14K10, 11G18 (primary), 14G35 (secondary), 2010 Mathematics Subject Classification:

ASJC Scopus subject areas

Mathematics(all)
Computational Mathematics
Mathematics(all)
Analysis
Mathematics(all)
Theoretical Computer Science
Mathematics(all)
Discrete Mathematics and Combinatorics
Mathematics(all)
Geometry and Topology
Mathematics(all)
Algebra and Number Theory
Mathematics(all)
Statistics and Probability
Mathematics(all)
Mathematical Physics

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

Research output: Contribution to journal › Article › Research › peer review

Gao, Z 2019, 'Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results', Forum of Mathematics, Sigma, vol. 7, e16. https://doi.org/10.1017/fms.2019.10

Gao, Z. (2019). Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results. Forum of Mathematics, Sigma, 7, Article e16. https://doi.org/10.1017/fms.2019.10

Gao Z. Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results. Forum of Mathematics, Sigma. 2019 May 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 ; Vol. 7.

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Research@Leibniz University