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Kodaira and Neron classified and described the geometry of the special fibers of the Neron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Neron list...
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