Counting sheaves using spherical codes
Counting sheaves using spherical codes
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使用球形代码计算滑轮数量
DOI：
10.4310/mrl.2013.v20.n2.a8
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
P. Michel
中科院分区：
文献类型：
--
作者：
'Etienne Fouvry;E. Kowalski;P. Michel
使用有限域上的黎曼假设和球码大小的界限，我们给出了关于有限域上曲线上几何不可约的椭圆中伸滑轮的几何同构类的数量的多项式大小相对于域大小的显式上限，该曲线是权重为 0 的点纯且具有有界分枝和秩。作为一个应用，我们表明，在有限域上定义的“随机”函数通常不能通过复杂度较小的滑轮迹函数的短线性组合来近似。
Using the Riemann Hypothesis over finite fields and bounds for the size of spherical codes, we give explicit upper bounds, of polynomial size with respect to the size of the field, for the number of geometric isomorphism classes of geometrically irreducible ell-adic middle-extension sheaves on a curve over a finite field which are pointwise pure of weight 0 and have bounded ramification and rank. As an application, we show that "random" functions defined on a finite field can not usually be approximated by short linear combinations of trace functions of sheaves with small complexity.