Geodesic
ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS
Forum of Mathematics, Sigma, Tome 7 (2019)

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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 logarithmic Ax theorem and the Ax-Lindemann theorem which we shall prove. All these bi-algebraic and transcendental results extend their counterparts for mixed Shimura varieties. In the end we briefly discuss the André–Oort and Zilber–Pink type problems for enlarged mixed Shimura varieties. 
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     author = {ZIYANG GAO},
     title = {ENLARGED {MIXED} {SHIMURA} {VARIETIES,} {BI-ALGEBRAIC} {SYSTEM} {AND} {SOME} {AX} {TYPE} {TRANSCENDENTAL} {RESULTS}},
     journal = {Forum of Mathematics, Sigma},
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     year = {2019},
     doi = {10.1017/fms.2019.10},
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ZIYANG GAO. ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.10

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