紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2018, 55(2), p. 369-384

TYPE NUMBERS OF QUATERNION HERMITIAN FORMS AND SUPERSINGULAR ABELIAN VARIETIES

Ibukiyama, Tomoyoshi

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2018-04

The word type number of an algebra means classically the number of isomorphism classes of maximal orders in the algebra, but here we consider quaternion hermitian lattices in a fixed genus and their right orders. Instead of inner isomorphism classes of right orders, we consider isomorphism classes realized by similitudes of the quaternion hermitian forms.The number T of such isomorphism classes are called type number or G-type number, where G is the group of quaternion hermitian similitudes. We express T in terms of traces of some special Hecke operators. This is a generalization of the result announced in [5] (I) from the principal genus to general lattices. We also apply our result to the number of isomorphism classes of any polarized superspecial abelian varieties which have a model over Fᴘ such that the polarizations are in a ”fixed genus of lattices”. This is a generalization of [8] and has an application to the number of components in the supersingular locus which are defined over Fᴘ.

10.18910/68357

68357

TYPE NUMBERS OF QUATERNION HERMITIAN FORMS AND SUPERSINGULAR ABELIAN VARIETIES

Ibukiyama, Tomoyoshi

Osaka University and Osaka City University, Departments of Mathematics

英語

2018-04

Osaka Journal of Mathematics

55

2

369

384

https://hdl.handle.net/11094/68357

10.18910/68357

https://doi.org/10.18910/68357