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摘要翻译：
设K是特征P>0的域，设q是P的幂。在一定的分支假设下，我们确定了K[t]\K[t^p]中的所有q(q-1)/2次多项式f，使得K(u)上f(t)-u的Galois群具有与PSL2(q)同构的传递正规子群。因此，我们描述了K[t]中的所有非p的幂次多项式f，使得f在K上是函数不可分解的，而f在K的一个扩张上是函数不可分解的。此外，除了一个分支设置（在配套论文ArXIV:0707.1837)中得到了处理）之外，我们描述了K[t]中所有非p的幂次不可分解多项式f，其意义是x-y是f(x)-f(y)在K[x，y]中唯一的绝对不可约因子。已知，当K是有限的时，多项式f是例外的当且仅当它在K的无穷多个有限扩张上诱导双射。
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英文标题：
《Polynomials with PSL(2) monodromy》
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作者：
Robert M. Guralnick and Michael E. Zieve
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
Let K be a field of characteristic p>0, and let q be a power of p. We determine all polynomials f in K[t]\K[t^p] of degree q(q-1)/2 such that the Galois group of f(t)-u over K(u) has a transitive normal subgroup isomorphic to PSL_2(q), subject to a certain ramification hypothesis. As a consequence, we describe all polynomials f in K[t], of degree not a power of p, such that f is functionally indecomposable over K but f decomposes over an extension of K. Moreover, except for one ramification setup (which is treated in the companion paper arxiv:0707.1837), we describe all indecomposable polynomials f in K[t] of non-p-power degree which are exceptional, in the sense that x-y is the only absolutely irreducible factor of f(x)-f(y) which lies in K[x,y]. It is known that, when K is finite, a polynomial f is exceptional if and only if it induces a bijection on infinitely many finite extensions of K.
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PDF链接：
https://arxiv.org/pdf/0707.1835
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