Errata to the Paper “False Hyperelliptic Surfaces with Section”
Errata to the Paper “False Hyperelliptic Surfaces with Section”
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论文“带截面的假超椭圆曲面”勘误表
DOI：
10.1002/mana.19961820115
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发表时间：
1996
影响因子：
1
通讯作者：
Y. Takeda
中科院分区：
文献类型：
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作者：
Y. Takeda
第3节中引理3.1的证明仅对v= 1有效。事实上，在v 2 2的情况下，推论3.3对引理的断言与超奇异性相矛盾。实际上，这个推论断言存在OC通过OC的非平凡扩张，使得其通过Frobenius k-态射的p次幂的拉回对于p 5 v不分裂，并且对于p 2 v分裂。然而，由于Ext '（Oc，Oc）= H'（C，Oc）并且由于Frobenius k-态射诱导H1（C，OC）上的零映射，任何这样的扩张的Frobenius k-态射的拉回都不分裂。因此，在第3节和第4节中的所有论证和断言中，v应该被理解为1。因此，在引言中所述的关于椭圆纤维化的问题仍然是开放的。
The proof of Lemma 3.1 in Section 3 is valid only for v= 1. In fact, in the case of v 2 2, the assertion of Corollary 3.3 to the lemma contradicts with the supersingularity. Indeed, this corollary asserted that there exists a nontrivial extension of OC by OC such that its pull-back by the p-th power of the Frobenius k-morphism does not split for p 5 v and splits for p 2 v. However, since Ext'(Oc, Oc)= H'(C, Oc) and since the Frobenius k-morphism induces the zero-mapping on H1 (C, OC), the pull-back by the Frobenius k-morphism of any such extension does split. Thus, in all arguments and assertions in Sections 3 and 4, v should be read as 1. Therefore the problem concerning elliptic fibrations stated in Introduction is still open.