Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1311-6008-0 |
Объём: | 76 страниц |
Масса: | 135 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In algebraic geometry, a semistable abelian variety is an abelian variety defined over a global or local field, which is characterized by how it reduces at the primes of the field. For an Abelian variety A defined over a field F with ring of integers R, consider the Neron model of A, which is a 'best possible' model of A defined over R. A semistable elliptic curve may be described more concretely as an elliptic curve that has bad reduction only of multiplicative type. Suppose E is an elliptic curve defined over the rational number field Q. It is known that there is a finite, non-empty set S of prime numbers p for which E has bad reduction modulo p. The latter means that the curve Ep obtained by reduction of E to the prime field with p elements has a singular point. Roughly speaking, the condition of multiplicative reduction amounts to saying that the singular point is a double point, rather than a cusp. Deciding whether this condition holds is effectively computable according to Tate's algorithm.
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