Codimension 2
From Mathematics
(→Cycles in codim 2, part I) |
(→Cycles in codim 2, part I) |
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* Remind of Lemma 2.1<ref name="Blo74"/> which has been discussed in the talk on Cech cohomology | * Remind of Lemma 2.1<ref name="Blo74"/> which has been discussed in the talk on Cech cohomology | ||
* Deduce the long exact sequence associated with the sequence of sheaves | * Deduce the long exact sequence associated with the sequence of sheaves | ||
| + | |||
<math> | <math> | ||
1 \rightarrow K_2 \rightarrow St \rightarrow \mathrm{SL} \rightarrow 1 | 1 \rightarrow K_2 \rightarrow St \rightarrow \mathrm{SL} \rightarrow 1 | ||
</math> | </math> | ||
| − | and | + | |
| + | and obtain a map | ||
| + | |||
| + | <math> | ||
| + | H^1(X, \mathrm{SL}_2(\mathcal{O}_X)) \rightarrow H^1(X, K_2(\mathcal{O}_X)). | ||
| + | </math> | ||
References: <ref name="Blo74"/>, (<ref name="Blo10"/>, §4) | References: <ref name="Blo74"/>, (<ref name="Blo10"/>, §4) | ||
