Specialization maps for Scholze's category of diamonds
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866908482572124160 |
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| author | Gleason, Ian |
| author_facet | Gleason, Ian |
| contents | We introduce the specialization map in Scholzes theory of diamonds. We consider v-sheaves that behave like formal schemes and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a Zariski site, and an etale site. When the kimberlite comes from a formal scheme, our sites recover the classical ones. We prove that unramified p-adic Beilinson--Drinfeld Grassmannians are kimberlites with finiteness and normality properties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_05483 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Specialization maps for Scholze's category of diamonds Gleason, Ian Algebraic Geometry Number Theory We introduce the specialization map in Scholzes theory of diamonds. We consider v-sheaves that behave like formal schemes and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a Zariski site, and an etale site. When the kimberlite comes from a formal scheme, our sites recover the classical ones. We prove that unramified p-adic Beilinson--Drinfeld Grassmannians are kimberlites with finiteness and normality properties. |
| title | Specialization maps for Scholze's category of diamonds |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2012.05483 |