Cycle classes and the syntomic regulator
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2010
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| _version_ | 1866910557985046528 |
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| author | Chiarellotto, B. Ciccioni, A. Mazzari, N. |
| author_facet | Chiarellotto, B. Ciccioni, A. Mazzari, N. |
| contents | Let $V=Spec(R)$ and $R$ be a complete discrete valuation ring of mixed characteristic $(0,p)$. For any flat $R$-scheme $X$ we prove the compatibility of the de Rham fundamental class of the generic fiber and the rigid fundamental class of the special fiber. We use this result to construct a syntomic regulator map $r:CH^i(X/V,2i-n)\to H^n_{syn}(X,i)$, when $X$ is smooth over $V$, with values on the syntomic cohomology defined by A. Besser. Motivated by the previous result we also prove some of the Bloch-Ogus axioms for the syntomic cohomology theory, but viewed as an absolute cohomology theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1006_0132 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Cycle classes and the syntomic regulator Chiarellotto, B. Ciccioni, A. Mazzari, N. Algebraic Geometry K-Theory and Homology 14F43, 14F30, 19F27 Let $V=Spec(R)$ and $R$ be a complete discrete valuation ring of mixed characteristic $(0,p)$. For any flat $R$-scheme $X$ we prove the compatibility of the de Rham fundamental class of the generic fiber and the rigid fundamental class of the special fiber. We use this result to construct a syntomic regulator map $r:CH^i(X/V,2i-n)\to H^n_{syn}(X,i)$, when $X$ is smooth over $V$, with values on the syntomic cohomology defined by A. Besser. Motivated by the previous result we also prove some of the Bloch-Ogus axioms for the syntomic cohomology theory, but viewed as an absolute cohomology theory. |
| title | Cycle classes and the syntomic regulator |
| topic | Algebraic Geometry K-Theory and Homology 14F43, 14F30, 19F27 |
| url | https://arxiv.org/abs/1006.0132 |