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I am interested in the conjecture suggesting that many reductions of a smooth complex projective variety are ordinary, as mentioned in Remark 5.1 of the paper by Mustaţă and Srinivas:

Ordinary varieties and the comparison between multiplier ideals and test ideals.

I am looking for other references where a general form of this conjecture or question is explicitly stated, even for specific cases like abelian varieties. I have not found any in Bloch-Kato or Ogus, or in the text by Chambert-Loir cited in Mustaţă-Srinivas.

Additionally, I am interested in understanding the broader context of this conjecture:

•   What are the main implications if the conjecture holds in general?
•   Is this conjecture related to other known conjectures in the field?
•   How does it fit within the larger landscape of algebraic geometry and arithmetic geometry?

Any insights, references, or explanations on where this conjecture “lives” within the mathematical literature would be greatly appreciated.

Thank you for your help!

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