تقرير
Motivic congruences and Sharifi's conjecture
| العنوان: | Motivic congruences and Sharifi's conjecture |
|---|---|
| المؤلفون: | Rivero, Óscar, Rotger, Victor |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11F33, 11F67, 11F80 |
| الوصف: | Let $f$ be a cuspidal eigenform of weight two and level $N$, let $p\nmid N$ be a prime at which $f$ is congruent to an Eisenstein series and let $V_f$ denote the $p$-adic Tate module of $f$. Beilinson constructed a class $\kappa_f\in H^1(\mathbb Q,V_f(1))$ arising from the cup-product of two Siegel units and proved a striking relationship with the first derivative $L'(f,0)$ at the near central point $s=0$ of the $L$-series of $f$, which led him to formulate his celebrated conjecture. In this note we prove two congruence formulae relating the "motivic part" of $L'(f,0) \,(\mathrm{mod} \, p)$ and $L''(f,0) \,(\mathrm{mod} \, p)$ with circular units. The proofs make use of delicate Galois properties satisfied by various integral lattices within $V_f$ and exploits Perrin-Riou's, Coleman's and Kato's work on the Euler systems of circular units and Beilinson--Kato elements and, most crucially, the work of Sharifi, Fukaya--Kato and Ohta. Comment: 22 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2101.09972 |
| رقم الأكسشن: | edsarx.2101.09972 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |