تقرير
Algebraic K-theory of real topological K-theory
| العنوان: | Algebraic K-theory of real topological K-theory |
|---|---|
| المؤلفون: | Angelini-Knoll, Gabriel, Ausoni, Christian, Rognes, John |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Topology, Mathematics - K-Theory and Homology, 19D50, 19D55, 55Q51, 55P43, 14F30 (Primary) 19E20, 13D03, 55N15, 55Q10, 55T25 (Secondary) |
| الوصف: | We determine the A(1)-homotopy of the topological cyclic homology of the connective real K-theory spectrum ko. The answer has an associated graded that is a free F_2[v_2^4]-module of rank 52, on explicit generators in stems -1 \le * \le 30. The calculation is achieved by using prismatic and syntomic cohomology of ko as introduced by Hahn-Raksit-Wilson, extending work of Bhatt-Morrow-Scholze from the case of classical commutative rings to E_\infty rings. A new feature in our case is that there are nonzero differentials in the motivic spectral sequence from syntomic cohomology to topological cyclic homology. Comment: 52 pages, 12 figures, 1 table. Conjecture B from v1 is proved in v2, along with other improvements |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.11463 |
| رقم الأكسشن: | edsarx.2309.11463 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |