Rank 2 local systems and abelian varieties
| العنوان: | Rank 2 local systems and abelian varieties |
|---|---|
| المؤلفون: | Ambrus Pál, Raju Krishnamoorthy |
| المصدر: | Selecta Mathematica. 27 |
| بيانات النشر: | Springer Science and Business Media LLC, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Pure mathematics, Conjecture, Mathematics - Number Theory, Rank (linear algebra), Absolutely irreducible, General Mathematics, 14K15, 14G35, 11G10, 010102 general mathematics, General Physics and Astronomy, 01 natural sciences, Mathematics - Algebraic Geometry, Monodromy, 0103 physical sciences, FOS: Mathematics, Number Theory (math.NT), 010307 mathematical physics, 0101 mathematics, Projective test, Variety (universal algebra), Abelian group, Algebraic Geometry (math.AG), Mathematics |
| الوصف: | Let $X/\mathbb{F}_{q}$ be a smooth geometrically connected variety. Inspired by work of Corlette-Simpson over $\mathbb{C}$, we formulate a conjecture that absolutely irreducible rank 2 local systems with infinite monodromy on $X$ come from families of abelian varieties. When $X$ is a projective variety, we prove a Lefschetz-style theorem for abelian schemes of $\text{GL}_2$-type on $X$, modeled after a theorem of Simpson. If one assumes a strong form of Deligne's ($p$-adic) \emph{companions conjecture} from Weil II, this implies that our conjecture for projective varieties also reduces to the case of projective curves. We also answer affirmitavely a question of Grothendieck on extending abelian schemes via their $p$-divisible groups. Comment: 29 pages, comments very welcome. v3: completely reorganized, minor errors fixed. v4: final version |
| تدمد: | 1420-9020 1022-1824 |
| DOI: | 10.1007/s00029-021-00669-8 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51047b05fed74fa2663f049a1153390f https://doi.org/10.1007/s00029-021-00669-8 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....51047b05fed74fa2663f049a1153390f |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 14209020 10221824 |
|---|---|
| DOI: | 10.1007/s00029-021-00669-8 |