Tohoku Mathematical Journal
2013
September
SECOND SERIES VOL. 65, NO. 3

Tohoku Math. J.
65 (2013), 357-371

Title NON-EXISTENCE OF CERTAIN CM ABELIAN VARIETIES WITH PRIME POWER TORSION

Author Yoshiyasu Ozeki

(Received December 21, 2011, revised November 2, 2012)
Abstract. In this paper, we study a conjecture of Rasmussen and Tamagawa, on the finiteness of the set of isomorphism classes of abelian varieties with constrained prime power torsion. Our result is related with abelian varieties which have complex multiplication over their fields of definition.

Mathematics Subject Classification. Primary 11G10; Secondary 14K22.
Key words and phrases. Abelian varieties, compatible systems.

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