论文标题
Anderson T-Motives简介：调查
Introduction to Anderson t-motives: a survey
论文作者
论文摘要
这是对安德森T-动物的调查 - 德林菲尔德模块的高维概括。它们是通过假想的二次场乘以乘积的阿贝尔品种的功能场类似物。我们描述了他们的晶格，$ h^1 $和$ h_1 $，张量产品，二元函数和二元定理，有限特征的德林菲尔德模块的内态性，以及其某种类型的L函数。此外，我们介绍了仿射方程的概念，$ t $ - 可见的$ \ bbb f_q [[t]] $ - 模块，功能场案例中的自动序列，siegel矩阵的类似物作为旗帜品种元素的类似物，以及其他一些概念（继续）。给出了许多明确计算的示例，并指出了一些基本研究问题。一些结果（第16节； 19节）显然是新的。
This is a survey on Anderson t-motives -- high-dimensional generalizations of Drinfeld modules. They are the functional field analogs of abelian varieties with multiplication by an imaginary quadratic field. We describe their lattices, their groups $H^1$ and $H_1$, their tensor products, the duality functor and the duality theorem, endomorphisms of Drinfeld modules in finite characteristic, and their L-functions of a certain type. Further on, we introduce the notion of affine equations, $T$-divisible $\Bbb F_q[[T]]$-modules, holonomic sequences in the functional field case, analogs of Siegel matrices as elements of flag varieties, and some other notions (to be continued). Many examples of explicit calculations are given, some elementary research problems are stated. Some results (Sections 16; 19) are apparently new.
