Cubic Structures and Ideal Class Groups
نویسنده
چکیده
We establish a generalization of Breen’s theory of cubic structures on line bundles over group schemes. We study such “n-cubic structures” inductively using multiextensions. As a result we obtain information on the set of isomorphism classes of line bundles with n-cubic structures over finite multiplicative group schemes over Spec (Z) by relating this set to certain corresponding eigenspaces of ideal class groups of cyclotomic fields.
منابع مشابه
Galois Modules, Ideal Class Groups and Cubic Structures
We establish a connection between the theory of cyclotomic ideal class groups and the theory of “geometric” Galois modules and obtain results on the Galois module structure of coherent cohomology groups of Galois covers of varieties over Z. In particular, we show that an invariant that measures the obstruction to the existence of a virtual normal integral basis for the coherent cohomology of su...
متن کاملOn the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields
Given any family of cubic fields defined by local conditions at finitely many primes, we determine the mean number of 2-torsion elements in the class groups and narrow class groups of these cubic fields, when they are ordered by their absolute discriminants. For an order O in a cubic field, we study the three groups: Cl2(O), the group of ideal classes of O of order 2; Cl2 (O), the group of narr...
متن کاملCharacterization and axiomatization of all semigroups whose square is group
In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup). Finally, several equivalent conditions ...
متن کاملFinite groups admitting a connected cubic integral bi-Cayley graph
A graph is called integral if all eigenvalues of its adjacency matrix are integers. Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$. In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.
متن کاملExamples of norm-Euclidean ideal classes
In [11], Lenstra defined the notion of Euclidean ideal class. Using a slight modification of an algorithm described in [12], we give new examples of number fields with norm-Euclidean ideal classes. Extending the results of Cioffari ([5]), we also establish the complete list of pure cubic number fields which admit a norm-Euclidean ideal class.
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 2005