Group, commutative

The family of phase transformations U(a) = expia, where a single parameter a may run continuously over real numbers, forms a unitary Abelian (commutative) group known as the [/( ) group. Compare 2.8.2.5... [Pg.166]

CGS] F. Oort, Commutative group schemes. Lecture Notes in Math. 15, Springer-Verlag (1966). [Pg.55]

All group schemes will be commutative group schemes. [Pg.83]

Since rings as well as modules are built from commutative groups and groups are identified with thin schemes (via the group correspondence) one may view the notion of a ring and the one of a module as part of thin scheme theory . [Pg.153]

It is easy to see that the restriction of the complex addition to M/L is an operation on M/L. Moreover, one verifies easily that, with respect to this addition, M/L is a commutative group. [Pg.157]

We say that G is a commutative group object if moreover s is a commutative composition ... [Pg.7]

This set E°(A,B) of equivalence classes can be equlped with the structure of a commutative group (In case n = l Baer-multlpllcatlon, of, [8],... [Pg.28]

THEOREM (l6.l) (CARTIER-SHATZ formula) Let T be a prescheme. Let N be a commutative group scheme over T, such that for every affine open set UcT, N = Spec(Ep) where is a finitely generated,... [Pg.83]

REMARK Let S be a locally noetherian prescherae, T 6 (Sch/S) and M a finite, flat, commutative group scheme over S. The theorem in this case reads ... [Pg.83]

PROPOSITION (16.3)5 Let T = Spec(B), N = Spec(E) a commutative group scheme over T such that E is finitely generated and projective over B. There exists a (functorial) isomorphism... [Pg.87]

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