A supersingular coincidence

The Ramanujan Journal - Tập 59 - Trang 609-613 - 2021
G. K. Sankaran1
1Department of Mathematical Sciences, University of Bath, Bath, UK

Tóm tắt

The 15 primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 are called the supersingular primes: they occur in several contexts in number theory and also, strikingly, they are the primes that divide the order of the Monster. It is also known that the moduli space of (1, p)-polarised abelian surfaces is of general type for these primes. In this note, we explain that apparently coincidental fact by relating it to other number-theoretic occurences of the supersingular primes.

Tài liệu tham khảo

Gross, M., Popescu, S.: The moduli space of \((1,11)\)-polarized Abelian surfaces is unirational. Compos. Math. 126, 1–23 (2001)

He, Y.-H., McKay, J.: Sporadic and exceptional. arXiv:1505.06742, (2015)

Hulek, K., Kahn, C., Weintraub, S.: Moduli Spaces of Abelian Surfaces: Compactification, Degenerations, and Theta Functions. Expositions in Mathematics, vol. 12. de Gruyter, Berlin (1993)