We study the following question: given a global field $ F $ and finite group $ G $, what is the
minimal $ r $ such that there exists a finite extension $ K/F $ with $\mathrm {Aut}(K/F)\cong G …

For a fixed prime power qq and natural number dd, we consider a random polynomial f= xn+
an− 1 (t) xn− 1+⋯+ a 1 (t) x+ a 0 (t)∈ F qtxf= x^ n+ a_ n-1 (t) x^ n-1+ ⋯+ a_1 (t) x+ a_0 (t) ∈ F …

For each nonnegative integer $ g $, we classify the ramification types and monodromy
groups of indecomposable coverings of complex curves $ f: X\to Y $ where $ X $ has genus …

We prove a large finite field version of the Boston–Markin conjecture on counting Galois
extensions of the rational function field with a given Galois group and the smallest possible …

A note on unramified extensions of quadratic number fields Page 1 A note on unramified
extensions of quadratic number fields Kwang-Seob Kim and Joachim König Abstract We show …

We prove that for any prime p> 2, q= p ν a power of p, n≥ p and G= S n or G= A n (symmetric
or alternating group), there exists a Galois extension K/F q (T) ramified only over∞ with Gal …