The inverse Galois problem for PSL_2(F_p)

Abstract

We show that the simple group PSL_2(F_p) occurs as the Galois group of an extension of the rationals for all primes p>3. We obtain our Galois extensions by studying the Galois action on the second etale cohomology groups of a specific elliptic surface.

Cited by in corpus (5)

• Sieves and the Minimal Ramification Problem
• Chow's theorem for semi-abelian varieties and bounds for splitting fields of algebraic tori
• Stronger arithmetic equivalence
• Rigidity for F_4(p)
• On the number of ramified primes in specializations of function fields over $\mathbb{Q}$