On the rational K_2 of a curve of GL_2-type over a global field of positive characteristic
On the rational K_2 of a curve of GL_2-type over a global field of positive characteristic
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正特征全局场上GL_2型曲线的有理K_2
DOI：
10.1017/is014006024jkt272
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发表时间：
2014
影响因子：
--
通讯作者：
Satoshi Kondo and Takuya Yamauchi
中科院分区：
文献类型：
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作者：
Masataka Chida;Satoshi Kondo and Takuya Yamauchi
如果是整体域k上光滑曲线X的积分模型，则存在比较和X的K-理论的局部化序列。我们证明了K1（）有理地注入到K1（X）中，通过证明在局部化序列中的前一个边界映射是有理满射，对于“GL 2型”的X和正特征标k不为2。通过实例证明了相对G1项可以具有大秩。这样的曲线的例子包括非等平凡椭圆曲线、德林费尔德模曲线和秩为2的-椭圆层的模。
If is an integral model of a smooth curve X over a global field k, there is a localization sequence comparing the K-theory of and X. We show that K1 () injects into K1(X) rationally, by showing that the previous boundary map in the localization sequence is rationally a surjection, for X of “GL2 type” and k of positive characteristic not 2. Examples are given to show that the relative G1 term can have large rank. Examples of such curves include non-isotrivial elliptic curves, Drinfeld modular curves, and the moduli of -elliptic sheaves of rank 2.