On Primitive and Realisable Classes
نویسنده
چکیده
Let S be a scheme, and letGbe a ¢nite, £at, commutative group scheme over S. In this paper we show that (subject to a mild technical assumption) every primitive class in Pic(G) is realisable. This gives an af¢rmative answer to a question of Waterhouse. We also discuss applications to locally free classgroups and to Selmer groups of Abelian varieties. Mathematics Subject Classi¢cations (2000). 11Gxx, 11Rxx, 14Kxx.
منابع مشابه
Bond Graphs III: Bond Graphs and Electrical Networks
Electrical networks are defined and a definition of when a bond graph and an electrical network are equivalent is given. Bond graphs and electrical networks are defined to be primitive if they contain no transformers or gyrators. A bond graph is defined to be realisable if it is equivalent to an electrical network and primitively realisable if it is equivalent to a primitive electrical network....
متن کاملBrandt extensions and primitive topologically periodic inverse topological semigroups
In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...
متن کاملOn the Relative Galois Module Structure of Rings of Integers in Tame Extensions
Let F be a number field with ring of integers OF and let G be a finite group. We describe an approach to the study of the set of realisable classes in the locally free class group Cl(OF G) of OF G that involves applying the work of the second-named author in the context of relative algebraic K theory. For a large class of soluble groups G, including all groups of odd order, we show (subject to ...
متن کاملResults Concerning the Decision RegionsRealisable by a Two - Layer
A few results concerning the number of realisable and non-realisable con-gurations are derived. Given that a two-layer perceptron has a number n of real valued inputs, m hidden nodes and one output node, a lower bound on the number of non-realisable conngurations is derived. It is also shown that the fraction of non-realisable conngurations asymptotically tends to one as m tends to innnity. Bou...
متن کاملRanks of the Sylow 2-Subgroups of the Classical Simple Groups
0. Introduction A 2-group is called realisable if it is isomorphic to a Sylow 2-subgroup of a finite simple group. It is well known that very few 2-groups are realisable (see [HL], [M]). In order to understand such realisable 2-groups, one would like to find a set of invariance of 2-groups which enables us to differentiate Ω1 (the set of realisable 2-groups) from Ω2 (the set of non-realisable 2...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001