تقرير
Uniqueness of indecomposable idempotents in algebras with involution
| العنوان: | Uniqueness of indecomposable idempotents in algebras with involution |
|---|---|
| المؤلفون: | Karemaker, Valentijn, Tamagawa, Akio, Yu, Chia-Fu |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, 16H20 (14K12 11E39 11G10) |
| الوصف: | We prove uniqueness of a decomposition of $1$ into indecomposable Hermitian idempotents in an order of a finite-dimensional $\mathbb{Q}$-algebra with positive involution, by generalising a result of Eichler on unique decomposition of lattices. We use this result to prove that polarised abelian varieties over any field admit a unique decomposition into indecomposable polarised abelian subvarieties, a result previously shown by Debarre and Serre with different methods and over algebraically closed fields. We prove that an analogous uniqueness result holds true for arbitrary polarised integral Hodge structures, and derive a consequence for their automorphism groups. Comment: 12 pages |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2402.09323Test |
| رقم الانضمام: | edsarx.2402.09323 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |