{'fraction_non_alphanumeric': 0.018564356435643563, 'fraction_numerical': 0.0012376237623762376, 'mean_word_length': 4.992592592592593, '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}}
Questions on p-torsion of hyperelliptic curves

We describe geometric questions raised by recent work on the porsion of Jacobians of curves defined over an algebraically closed field k of characteristicp. These questions involve invariants of thep-torsion such as thep-rank ora-number. Such invariants are well-understood and have been used to define stratifications of the moduli space Ag of principally polarized abelian varieties of dimension g. A major open problem is to understand how the Torelli locus intersects such strata in Ag. In [3], we show that some of these strata intersect the image of the hyperelliptic locus under the Torelli map. This work relies upon geometric results on the configurations of branch points for non-ordinary hyperelliptic curves and raises some new geometric questions.