The Ideal Class & Minkowski's Theorem Flashcards

1
Q

equivalent ideals

A

there exist α,β in O_K such that (α)I=(β)J

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2
Q

ideal classes

A

equivalence classes of ideals in O_K

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3
Q

class number

A

number of ideal classes

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4
Q

ideal class group

A

group of ideal classes

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5
Q

lattice

A

abelian subgroup m_1v_1+m_2v_2 where m_i integers and v_i linearly independent (basis of R^2)

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6
Q

generators of lattice

A

v_1 and v_2

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7
Q

fundamental domain of lattice

A

a_1 a_2 in [0,1)

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8
Q

covolume of lattice

A

volume of fundamental domain/ det of P=(v_1 v_2)

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9
Q

convex

A

λp + (1-λ)q in X

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10
Q

centrally symmetric

A

-p in X

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