任意特征的代数闭域乘法群的覆盖
Covers of Multiplicative Groups of Algebraically Closed Fields of Arbitrary Characteristic
摘要：
我们表明，代数类似物的通用群覆盖，满射群同态从一个$\mathbb{Q}$ -向量空间$F^{\times}$与“标准内核”，确定了同构的代数结构的特点和超越度的$F$，并在积极的特点，限制覆盖有限域。这推广了“Covers of the乘法群of an代数闭域of Characteristic Zero”（B. Zilber，JLMS 2007），我们的证明填补了那里给出的证明中的一个漏洞。
英文摘要：
We show that algebraic analogues of universal group covers, surjective group homomorphisms from a $\mathbb{Q}$-vector space to $F^{\times}$ with "standard kernel", are determined up to isomorphism of the algebraic structure by the characteristic and transcendence degree of $F$ and, in positive characteristic, the restriction of the cover to finite fields. This extends the main result of "Covers of the Multiplicative Group of an Algebraically Closed Field of Characteristic Zero" (B. Zilber, JLMS 2007), and our proof fills a hole in the proof given there.
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