论文标题
在某些Abelian品种中的方程式系统上
On Some Systems of Equations in Abelian Varieties
论文作者
论文摘要
我们解决了Abelian指数 - 代数封闭度猜想的案例，这是由于Zilber的作品而建立的，这是一个猜想和Kirby引起的，该猜想预测了涉及代数操作的方程式的足够条件，以及涉及代数型的方程式，并且可以在Abelian品种的指数上绘制，以便在复数中可解置。更确切地说，我们表明，猜想适用于Abelian品种$ a $的切线捆绑包，该捆绑是$ a $ a $ a $ a $ a $ a and代数的线性子空间的产物。这是由Zilber和Bays-kirby的工作激发的，该作品确定对猜想的积极答案将暗示某些结构对复数的准确性。我们的证明使用来自同源性（杯赛和交叉点之间的二元性），差异拓扑（横向性）和O最小性（Hausdorff限制的可确定性）的各种技术，因此我们试图提供独立的博览会。
We solve a case of the Abelian Exponential-Algebraic Closedness Conjecture, a conjecture due to Bays and Kirby, building on work of Zilber, which predicts sufficient conditions for systems of equations involving algebraic operations and the exponential map of an abelian variety to be solvable in the complex numbers. More precisely, we show that the conjecture holds for subvarieties of the tangent bundle of an abelian variety $A$ which split as the product of a linear subspace of the Lie algebra of $A$ and an algebraic variety. This is motivated by work of Zilber and of Bays-Kirby, which establishes that a positive answer to the conjecture would imply quasiminimality of certain structures on the complex numbers. Our proofs use various techniques from homology (duality between cup product and intersection), differential topology (transversality) and o-minimality (definability of Hausdorff limits), hence we have tried to give a self-contained exposition.
