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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.21082 |
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Table of Contents:
- In the classical theory for coherent sheaves, the only missing piece in the Grothendieck six-functor formalism picture is $j_!$ for an open immersion $j$. Towards fixing this gap, Deligne proposed a construction of $j_!$ by extending the sheaf class to pro sheaves, while Clausen-Scholze provided another solution by extending the sheaf class to solid modules. In this work, we prove that Deligne's construction coincides with the Clausen-Scholze construction via a natural functor, whose restriction to the full subcategory of Mittag-Leffler pro-systems is fully faithful.