Monodromy of Airy and Kloosterman sheaves
Monodromy of Airy and Kloosterman sheaves
复制标题
艾里滑轮和克洛斯特曼滑轮的单向性
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
O. Such
中科院分区：
文献类型：
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作者：
O. Such
该方程的简单性使得这些超椭圆曲线特别适合于需要更高亏格曲线的显式计算机计算。另一方面，方程的特殊形式提出了一个问题，即这些曲线有多普遍或随机（如果有的话）。例如，所有这些曲线都有2秩0。一般性的问题可以更精确地重述为一族曲线的单值群的问题。让我们用K表示域k（ai），其中ai是超椭圆曲线族C的可变参数。设l = 2，则-adic单值群是Gal（Ksep/K）在H1（C <$KK <$，Ql）上作用的象.曲线族C的许多性质由几何单值群Ggeom来描述，它是子群Gal（Ksep/Kk）的象的Zapriki闭包.例如，如果族C的几何单值群是有限的，则族C中的所有曲线都是超奇异的。我们证明，事实恰恰相反。
The simplicity of this equation makes these hyperelliptic curves particularly well suited for explicit computer calculations requiring higher genus curves. On the other hand, the special form of the equation raises the question of how generic or random, if at all, these curves are. For instance, all of these curves have 2-rank 0. The question of genericity can be restated more precisely as the question of the monodromy group of a family of curves. Let us denote by K the fieldk(ai), where ai are the variable parameters of a family C of hyperelliptic curves. Choosing l = 2, thel-adic monodromy group is the image of the action of Gal (Ksep/K) onH 1(C⊗K K̄,Ql). Many properties of a familyC of curves are described by the geometric monodromy groupGgeom, which is the Zariski closure of image of the subgroup Gal(Ksep/Kk̄). For instance, if the geometric monodromy group of a family C is finite, all curves in the familyC are supersingular. We prove that quite the opposite is true.