Share  Bookmark

 Download from



... 
 Funded by

Corollary 4.16: Let xe, ye, x]y 2 Aek, and let i, j 2 Z(`n), k, l 2 Zˆ (`n). Then we have: We will use the affine lifts of points in Bk[`] that we have introduced in Section 4.1 to study this notion. Let M0 = [`] L0 on Bk and QBk,M0 a theta structure for M0 [Mum67b] D. Mumford. On the equations defining abelian varieties. III. Invent. Math., 3:215244, 1967.
[Mum83] David Mumford. Tata lectures on theta I, volume 28 of Progress in Mathematics.
Birkhäuser Boston Inc., Boston, MA, 1983. With the assistance of C. Musili, M. Nori, E. Previato and M. Stillman.
[Mum84] David Mumford. Tata lectures on theta II, volume 43 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, 1984. Jacobian theta functions and differential equations, With the collaboration of C. Musili, M. Nori, E.
[Smi08] Benjamin Smith. Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves. Smart, Nigel (ed.), Advances in cryptology  EUROCRYPT 2008. 27th annual international conference on the theory and applications of cryptographic techniques, Istanbul, Turkey, April 1317, 2008. Proceedings. Berlin: Springer. Lecture Notes in Computer Science 4965, 163180 (2008)., 2008.