تقرير
On Hopkins' Picard group
| العنوان: | On Hopkins' Picard group |
|---|---|
| المؤلفون: | Barthel, Tobias, Schlank, Tomer M., Stapleton, Nathaniel, Weinstein, Jared |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Topology, Mathematics - Algebraic Geometry, Mathematics - Number Theory |
| الوصف: | We compute the algebraic Picard group of the category of $K(n)$-local spectra, for all heights $n$ and all primes $p$. In particular, we show that it is always finitely generated over $\mathbb{Z}_p$ and, whenever $n \geq 2$, is of rank $2$, thereby confirming a prediction made by Hopkins in the early 1990s. In fact, with the exception of the anomalous case $n=p=2$, we provide a full set of topological generators for these groups. Our arguments rely on recent advances in $p$-adic geometry to translate the problem to a computation on Drinfeld's symmetric space, which can then be solved using results of Colmez--Dospinescu--Niziol. Comment: 46 pages; all comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.20958 |
| رقم الأكسشن: | edsarx.2407.20958 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |