3 problems

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Murty–Patankar conjecture on absolutely simple reductions of abelian varieties
Murty–Patankar conjecture. The abelian variety $B$ has absolutely simple reduction for a density one set of primes up to a finite extension if and only if its endomorphism ring is…
Conjecturerefutedabelian-varieties endomorphism-rings reduction-mod-primesarXiv posted 2 days ago
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Achter–Howe conjecture for split abelian surfaces
Achter–Howe conjecture. There exists a positive constant $C_A$ such that
Conjectureopenabelian-surfaces arithmetic-statistics reduction-mod-primesarXiv posted 2 days ago
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Murty–Patankar–Zywina conjecture on geometric simplicity
Murty–Patankar–Zywina conjecture. Possibly after replacing $L$ by a finite extension $L'/L$ ,
Conjectureopenabelian-varieties complex-multiplication reduction-mod-primesarXiv posted 2 days ago

Murty–Patankar conjecture on absolutely simple reductions of abelian varieties