We show that many quadratic binomial functions on a finite field of characteristic 2 are not APN infinitely often. This is of interest in the light of recent discoveries of new families of quadratic binomial APN functions. The proof uses the Weil bound from algebraic geometry.
Appendix to ``Deligne's integrality theorem in unequal characteristic and rational points over finite fields'' by Hélène Esnault
On the faithfulness of parabolic cohomology as a Hecke module over a finite field
Counting points on varieties over finite fields of small characteristic
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