Non-commutative approach to the density of ordinary reduction
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The goal of this paper is to give a new non-commutative approach to Serre's ordinary density conjecture. We prove that ordinary reduction is inherited at almost all finite primes for a derived equivalent of smooth proper varieties over a number field and using the techniques of non-commutative algebraic geometry, we prove that Serre's ordinary density conjecture is true for cubic $4$-folds which contain $\mathbb{P}^2$.
Abstract
The goal of this paper is to give a new non-commutative approach to Serre's ordinary density conjecture. We prove that ordinary reduction is inherited at almost all finite primes for a derived equivalent of smooth proper varieties over a number field and using the techniques of non-commutative algebraic geometry, we prove that Serre's ordinary density conjecture is true for cubic $4$-folds which contain $\mathbb{P}^2$.