Proves irreducibility for most primes in 5-dim Galois compatible systems and uses it to verify the codimension-1 Tate conjecture for elliptic surfaces in six families for all but finitely many primes.
A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Ar- eas
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Five-dimensional compatible systems and the Tate conjecture for elliptic surfaces
Proves irreducibility for most primes in 5-dim Galois compatible systems and uses it to verify the codimension-1 Tate conjecture for elliptic surfaces in six families for all but finitely many primes.