KAROUBI’S RELATIVE CHERN CHARACTER, THE RIGID SYNTOMIC REGULATOR, AND THE BLOCH–KATO EXPONENTIAL MAP
We construct a variant of Karoubi’s relative Chern character for smooth separated schemes over the ring of integers in a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\ge...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2014-08-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509414000218/type/journal_article |
| Summary: | We construct a variant of Karoubi’s relative Chern character for smooth separated schemes over the ring of integers in a
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p$
-adic field, and prove a comparison with the rigid syntomic regulator. For smooth projective schemes, we further relate the relative Chern character to the étale
$p$
-adic regulator via the Bloch–Kato exponential map. This reproves a result of Huber and Kings for the spectrum of the ring of integers, and generalizes it to all smooth projective schemes as above. |
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| ISSN: | 2050-5094 |