Report
Linear relations of p-adic periods of 1-motives (thesis)
| العنوان: | Linear relations of p-adic periods of 1-motives (thesis) |
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| المؤلفون: | Mohajer, Mohammadreza |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, 14C30, 11S80, 14F30, 32G20, 14Kxx, 14K20, 14L05, 11G25, 14F42, 14C15 |
| الوصف: | In this thesis, we aim to develop p-adic analogs of known results for classical periods, focusing specifically on 1-motives. We establish an integration theory for 1-motives with good reductions, which generalizes the Colmez-Fontaine-Messing p-adic integration for abelian varieties with good reductions. We also compare the integration pairing with other pairings such as those induced by crystalline theory. Additionally, we introduce a formalism for periods and formulate p-adic period conjectures related to p-adic periods arising from this integration pairing. Broadly, our p-adic period conjecture operates at different depths, with each depth revealing distinct relations among the p-adic periods. Notably, the classical period conjecture (Kontsevich-Zanier conjecture over $\bar{\mathbb{Q}}$) for 1-periods fits within our framework, and, according to the classical subgroup theorem of Huber-W\"ustholz for 1-motives, the conjecture for classical periods of 1-motives holds true at depth 1. Finally, we identify three $\mathbb{Q}$-structures arising from $\bar{\mathbb{Q}}$-rational points of the formal p-divisible group associated with a 1-motive $M$ with a good reduction at $p$, and we prove p-adic period conjectures at depths 2 and 1, relative to periods induced by the p-adic integration of $M$ and these $\mathbb{Q}$-structures. Our proof involves a p-adic version of the subgroup theorem that we obtain for 1-motives with good reductions. Comment: This thesis was submitted by the author in 2024 in partial fulfillment of the requirements for the degree of Ph.D. in Mathematics at the University of Ottawa |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.20381/ruor-30802 |
| URL الوصول: | http://arxiv.org/abs/2411.03118 |
| رقم الانضمام: | edsarx.2411.03118 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.20381/ruor-30802 |
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