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01.01.1970 (Thursday)

NT Internal number theory seminar: How common is formal complex multiplication?

regular seminar Alex Torzewski (KCL)

at:
14:00 - 15:00
KCL, Strand
room: K2.31
abstract:

An elliptic curve over a characteristic zero field is said to have complex multiplication when its endomorphism ring is larger than Z ("E has extra endomorphisms"). Generic elliptic curves don't have complex multiplication. Often one tries to understand elliptic curves via their Tate modules. When the Tate module of E has extra endomorphisms we say E has formal complex multiplication. Over a number field, E has formal complex multiplication if and only if it has complex multiplication. Over a local field this need not be the case. How often does this happen?

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