Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | e16 |
| Seitenumfang | 65 |
| Fachzeitschrift | Forum of Mathematics, Sigma |
| Jahrgang | 7 |
| Publikationsstatus | Veröffentlicht - 27 Mai 2019 |
Abstract
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Theoretische Informatik
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
- Mathematik (insg.)
- Geometrie und Topologie
- Mathematik (insg.)
- Algebra und Zahlentheorie
- Mathematik (insg.)
- Statistik und Wahrscheinlichkeit
- Mathematik (insg.)
- Mathematische Physik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Forum of Mathematics, Sigma, Jahrgang 7, e16, 27.05.2019.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results
AU - Gao, Ziyang
N1 - © The Author 2019
PY - 2019/5/27
Y1 - 2019/5/27
N2 - 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.
AB - 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.
KW - math.AG
KW - math.NT
KW - 11G18, 11J81, 14G35, 14K10
KW - 11G18 (primary)
KW - 14G35 (secondary)
KW - 2010 Mathematics Subject Classification:
UR - http://www.scopus.com/inward/record.url?scp=85066738385&partnerID=8YFLogxK
U2 - 10.1017/fms.2019.10
DO - 10.1017/fms.2019.10
M3 - Article
VL - 7
JO - Forum of Mathematics, Sigma
JF - Forum of Mathematics, Sigma
M1 - e16
ER -