Reduction types of curves in p-adic families
Linfoot Number Theory Seminar
29th January 2025, 11:00 am – 12:00 pm
Fry Building, 2.04
Many invariants of curves over p-adic fields are computed from the mod p reduction of these curves. These invariants should vary continuously in p-adic families, which in this case means they are locally constant. For example, it is a consequence of Tate's algorithm that for an elliptic curve y^2 = x^3 + ax + b over Z_p, the reduction type, Tamagawa number and conductor all depend only on the classes of a and b mod p^N for some suitable N. In this talk I will explain this and similar results for general smooth projective curves.
Organisers: Holly Green, Besfort Shala
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