تقرير
Continuous K-Theory and Cohomology of Rigid Spaces
| العنوان: | Continuous K-Theory and Cohomology of Rigid Spaces |
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| المؤلفون: | Dahlhausen, Christian |
| المصدر: | manuscripta math. 173, 119-153 (2024) |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - K-Theory and Homology, Mathematics - Algebraic Geometry |
| الوصف: | We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete discretely valued field, its continuous K-groups vanish in degrees below the negative of the dimension. Likewise, the cohomology groups vanish in degrees above the dimension. The main result provides the existence of an isomorphism between the lowest possibly non-vanishing continuous K-group and the highest possibly non-vanishing cohomology group with integral coefficients. A key role in the proof is played by a comparison between cohomology groups of an admissible Zariski-Riemann space with respect to different topologies; namely, the rh-topology which is related to K-theory as well as the Zariski topology whereon the cohomology groups in question rely. Comment: v3: last submitted and final version |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00229-023-01470-x |
| URL الوصول: | http://arxiv.org/abs/1910.10437 |
| رقم الأكسشن: | edsarx.1910.10437 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s00229-023-01470-x |
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