{'fraction_non_alphanumeric': 0.08560311284046693, 'fraction_numerical': 0.013618677042801557, 'mean_word_length': 3.5575221238938055, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
CORRECTION TO “EXPLICIT POINTS ON THE LEGENDRE CURVE III”

10.1. Counterexample. Let k be a finite field of characteristic p, let W (k) be its ring of Witt vectors, and let σ : W (k) → W (k) be its Frobenius automorphism. Let C and D be smooth, projective curves over k. Part (2) of Theorem 5.2 is incorrect as stated. For a counterexample, let C = D = E where E is an ordinary elliptic curve over k = Fq, and take n = 1. Using well-known properties of elliptic curves, one finds that (( H(C)⊗W H(D) )F=p) /p ∼= Fp