共查询到20条相似文献,搜索用时 15 毫秒
1.
Let M be an irreducible projective variety, over an algebraically closed field k of characteristic zero, equipped with an action of a connected algebraic group S over k. Let E
G
be a principal G-bundle over M equipped with a lift of the action of S on M, where G is a connected reductive linear algebraic group. Assume that E
G
admits a reduction of structure group to a maximal torus TG. We give a necessary and sufficient condition for the existence of a T-reduction of E
G
which is left invariant by the action of S on E
G
. 相似文献
2.
Allison M. Pacelli 《Journal of Number Theory》2006,116(2):311-323
In this paper we construct, for any integers m and n, and 2?g?m-1, infinitely many function fields K of degree m over F(T) such that the prime at infinity splits into exactly g primes in K and the ideal class group of K contains a subgroup isomorphic to (Z/nZ)m-g. This extends previous results of the author and Lee for the cases g=1 and g=m. 相似文献
3.
Victor Bautista-Ancona 《Journal of Number Theory》2006,116(1):21-41
It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields that allow us to find a full list of all such field extensions for future reference. In doing so we correct some errors in earlier published literature. 相似文献
4.
Kalyan Chakraborty Anirban Mukhopadhyay 《Proceedings of the American Mathematical Society》2006,134(1):51-54
Let be an even positive integer. We show that there are polynomials with such that the ideal class group of the real quadratic extensions have an element of order .
5.
In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein–Maskit
combination theorem for Kleinian groups in which two Fuchsian subgroups are amalgamated along a parabolic subgroup. As a corollary,
we construct subgroups of the mapping class group (for all genera at least 2), which are isomorphic to non-abelian closed
surface groups in which all but one conjugacy class (up to powers) is pseudo-Anosov.
Received: October 2004 Revision: April 2005 Accepted: April 2005
C.J.L.’s work was partially supported by an NSF postdoctoral fellowship. A.W.R’s work was partially supported by an NSF grant. 相似文献
6.
Tauno Metsnkyl 《Expositiones Mathematicae》2007,25(4):325-340
This is a survey of a series of results about the class groups of algebraic number fields, with particular emphasis on two articles of Chebotarev [Eine Verallgemeinerung des Minkowski'schen Satzes mit Anwendung auf die Betrachtung der Körperidealklassen, Berichte der wissenschaftlichen Forschungsinstitute in Odessa 1(4) (1924) 17–20; Zur Gruppentheorie des Klassenkörpers, J. Reine Angew. Math. 161 (1929/30) 179–193; corrigendum, ibid. 164 (1931) 196] which seem to be almost forgotten. Their relationship to earlier work on the one hand, and to selected subsequent contributions on the other hand, is discussed. In this way, there emerges an interesting line of development, up to the present day, of results due to Kummer, Hasse, Leopoldt, Iwasawa, and others. More recent work treated here includes results by Cornell and Rosen (1981) and Lemmermeyer (2003) describing the structure of the class group under quite general conditions. 相似文献
7.
8.
S. Thangavelu 《Proceedings Mathematical Sciences》1991,101(3):169-177
A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory ofg-functions. 相似文献
9.
N. J. Michelacakis 《Proceedings of the American Mathematical Society》1996,124(11):3315-3323
In this note, we describe the Picard group of the class of compact, smooth, flat, projective varieties. In view of Charlap's work and Johnson's characterization, we construct line bundles over such manifolds as the holonomy-invariant elements of the Neron-Severi group of a projective flat torus covering the manifold. We prove a generalized version of the Appell-Humbert theorem which shows that the nontrivial elements of the Picard group are precisely those coming from the above construction. Our calculations finally give an estimate for the set of positive line bundles for such varieties.
10.
Christopher Allday Volker Hauschild Volker Puppe 《Transactions of the American Mathematical Society》2002,354(7):2971-2982
We prove that, under certain conditions, if a compact connected Lie group acts effectively on a closed manifold, then there is no fixed point. Because two of the main conditions are satisfied by any Hamiltonian action on a closed symplectic manifold, the theorem applies nicely to such actions. The method of proof, however, is cohomological; and so the result applies more generally.
11.
We prove that the mapping class group of a closed surface acts ergodically on connected components of the representation
variety corresponding to a connected compact Lie group.
Received: March 21, 2001 相似文献
12.
Ali Mouhib 《Mathematische Nachrichten》2016,289(14-15):1927-1933
We study the capitulation problem of the 2‐class group of some cyclic number fields M with large degree and 2‐class group isomorphic to . Precisely, we give the structure of the Galois group of the maximal unramified 2‐extension over M. 相似文献
13.
Czeslaw Bagiński 《代数通讯》2019,47(2):761-771
The modular isomorphism problem is settled for 3-groups of maximal class but two families of groups. Moreover, the conjecture that the ideals belonging to the lower central series of a group base are determined by the structure of the group algebra is refuted in greatest generality by virtue of a single group of order 81 of maximal class, and it is proved that the nilpotency class is determined by the structure of the group algebra for p-groups of maximal class. 相似文献
14.
We compute the Grothendieck group of non-commutative analogues of projective space bundles. Our results specialize to give
the Grothendieck groups of non-commutative analogues of projective spaces, and specialize to recover the Grothendieck group
of a usual projective space bundle over a regular noetherian separated scheme. As an application, we develop an intersection
theory for quantum ruled surfaces.
S. P. Smith was supported by NSF grants DMS 9701578 and 0070560
Received: March 2006 相似文献
15.
16.
Mark V. Losik 《Annals of Global Analysis and Geometry》1997,15(2):141-152
The cohomology of G-manifolds of the type M=P×
K
(G/H), where G is a reductive Lie group, H and N are its closed subgroups, H is a normal subgroup of N, K=N/H, and P is a smooth principal K-bundle, are considered. In the case when the Lie algebras of H and N are reductive, the differential graded algebra C(M) introduced in the previous paper with the same title and having the same minimal model as one of the algebra of G-invariant forms on M is investigated. Moreover, the main theorem on the cohomology algebra of C(M) is proved under weaker conditions than those of the previous paper. 相似文献
17.
The primary goal of this paper is to provide a rigorous theoretical justification of Cartans method of moving frames for arbitrary finite-dimensional Lie group actions on manifolds. The general theorems are based a new regularized version of the moving frame algorithm, which is of both theoretical and practical use. Applications include a new approach to the construction and classification of differential invariants and invariant differential operators on jet bundles, as well as equivalence, symmetry, and rigidity theorems for submanifolds under general transformation groups. The method also leads to complete classifications of generating systems of differential invariants, explicit commutation formulae for the associated invariant differential operators, and a general classification theorem for syzygies of the higher order differentiated differential invariants. A variety of illustrative examples demonstrate how the method can be directly applied to practical problems arising in geometry, invariant theory, and differential equations. 相似文献
18.
Roch Cassanas 《Journal of Functional Analysis》2009,256(1):91-128
Let G⊂O(n) be a compact group of isometries acting on n-dimensional Euclidean space Rn, and X a bounded domain in Rn which is transformed into itself under the action of G. Consider a symmetric, classical pseudodifferential operator A0 in L2(Rn) that commutes with the regular representation of G, and assume that it is elliptic on X. We show that the spectrum of the Friedrichs extension A of the operator is discrete, and using the method of the stationary phase, we derive asymptotics for the number Nχ(λ) of eigenvalues of A equal or less than λ and with eigenfunctions in the χ-isotypic component of L2(X) as λ→∞, giving also an estimate for the remainder term for singular group actions. Since the considered critical set is a singular variety, we recur to partial desingularization in order to apply the stationary phase theorem. 相似文献
19.
20.
We state and prove a Local Stable Manifold Theorem (Theorem 4.1) for non-linear stochastic differential systems with finite memory (viz. stochastic functional differential equations (sfde's)). We introduce the notion of hyperbolicity for stationary trajectories of sfde's. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary trajectory. The stable and unstable manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses infinite-dimensional multiplicative ergodic theory techniques developed by D. Ruelle, together with interpolation arguments. 相似文献