For every even N at least 6, the paper produces infinitely many SO_{N+1}-valued residual Galois representations that are SO_{N+1}-irreducible but GL_{N+1}-reducible, each with a geometric lift of Zariski-dense image.
The inverse Galois problem for orthogonal groups
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove many new cases of the Inverse Galois Problem for those simple groups arising from orthogonal groups over finite fields. For example, we show that the finite simple groups Omega_{2n+1}(p) and POmega_{4n}^+(p) both occur as the Galois group of a Galois extension of the rationals for all integers n>1 and all primes p>3. We obtain our representations by studying families of twists of elliptic curves and using some known cases of the Birch and Swinnerton-Dyer conjecture along with a big monodromy result of Hall.
fields
math.NT 1years
2019 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Lifting $G$-irreducible but $\mathrm{GL}_n$-reducible Galois representations
For every even N at least 6, the paper produces infinitely many SO_{N+1}-valued residual Galois representations that are SO_{N+1}-irreducible but GL_{N+1}-reducible, each with a geometric lift of Zariski-dense image.