共查询到20条相似文献,搜索用时 31 毫秒
1.
James Gillespie 《Mathematische Zeitschrift》2007,257(4):811-843
We put a monoidal model category structure on the category of chain complexes of quasi-coherent sheaves over a quasi-compact
and semi-separated scheme X. The approach generalizes and simplifies the method used by the author in (Trans Am Math Soc 356(8) 3369–3390, 2004) and
(Trans Am Math Soc 358(7), 2855–2874, 2006) to build monoidal model structures on the category of chain complexes of modules
over a ring and chain complexes of sheaves over a ringed space. Indeed, much of the paper is dedicated to showing that in
any Grothendieck category , any nice enough class of objects induces a model structure on the category Ch() of chain complexes. The main technical requirement on is the existence of a regular cardinal κ such that every object satisfies the following property: Each κ-generated subobject of F is contained in another κ-generated subobject S for which . Such a class is called a Kaplansky class. Kaplansky classes first appeared in Enochs and López-Ramos (Rend Sem Mat Univ Padova 107, 67–79,
2002) in the context of modules over a ring R. We study in detail the connection between Kaplansky classes and model categories. We also find simple conditions to put
on which will guarantee that our model structure is monoidal. We will see that in several categories the class of flat objects
form such Kaplansky classes, and hence induce monoidal model structures on the associated chain complex categories. We will
also see that in any Grothendieck category , the class of all objects is a Kaplansky class which induces the usual (non-monoidal) injective model structure on Ch(). 相似文献
2.
Let W and Z be Banach spaces, and let and be closed subspaces. Let be a subspace of , the Banach space of bounded linear operators from W* to Z**, containing . We describe, for and , all norm-preserving extensions of to the space in terms of convergence of convex combinations. We also characterize denting points of bounded convex subsets of Banach spaces
in similar terms. Various applications are presented.
Supported by Estonian Science Foundation Grant 5704. 相似文献
3.
For a smooth curve C it is known that a very ample line bundle on C is normally generated if Cliff() < Cliff(C) and there exist extremal line bundles (:non-normally generated very ample line bundle with Cliff() = Cliff(C)) with . However it has been unknown whether there exists an extremal line bundle with . In this paper, we prove that for any positive integers (g, c) with g = 2c + 5 and (mod 2) there exists a smooth curve of genus g and Clifford index c carrying an extremal line bundle with . In fact, a smooth quadric hypersurface section C of a general projective K3 surface always has an extremal line bundle with . More generally, if C has a line bundle computing the Clifford index c of C with , then C has such an extremal line bundle .
For all authors, this work was supported by Korea Research Foundation Grant funded by Korea Government (MOEHRD, Basic Reasearch
Promotion Fund)(KRF-2005-070-C00005). 相似文献
4.
Let be a C
2 map and let Spec(Y) denote the set of eigenvalues of the derivative DY
p
, when p varies in . We begin proving that if, for some ϵ > 0, then the foliation with made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case
of Jelonek’s Jacobian Conjecture for polynomial maps of
The first author was supported by CNPq-Brazil Grant 306992/2003-5. The first and second author were supported by FAPESP-Brazil
Grant 03/03107-9. 相似文献
5.
6.
Let be the classical kernel density estimator based on a kernel K and n independent random vectors X
i
each distributed according to an absolutely continuous law on . It is shown that the processes , , converge in law in the Banach space , for many interesting classes of functions or sets, some -Donsker, some just -pregaussian. The conditions allow for the classical bandwidths h
n
that simultaneously ensure optimal rates of convergence of the kernel density estimator in mean integrated squared error,
thus showing that, subject to some natural conditions, kernel density estimators are ‘plug-in’ estimators in the sense of
Bickel and Ritov (Ann Statist 31:1033–1053, 2003). Some new results on the uniform central limit theorem for smoothed empirical
processes, needed in the proofs, are also included.
相似文献
7.
The main result of this work is a Dancer-type bifurcation result for the quasilinear elliptic problem
Here, Ω is a bounded domain in denotes the Dirichlet p-Laplacian on , and is a spectral parameter. Let μ1 denote the first (smallest) eigenvalue of −Δ
p
. Under some natural hypotheses on the perturbation function , we show that the trivial solution is a bifurcation point for problem (P) and, moreover, there are two distinct continua, and , consisting of nontrivial solutions to problem (P) which bifurcate from the set of trivial solutions at the bifurcation point (0, μ1). The continua and are either both unbounded in E, or else their intersection contains also a point other than (0, μ1). For the semilinear problem (P) (i.e., for p = 2) this is a classical result due to E. N. Dancer from 1974. We also provide an example of how the union looks like (for p > 2) in an interesting particular case.
Our proofs are based on very precise, local asymptotic analysis for λ near μ1 (for any 1 < p < ∞) which is combined with standard topological degree arguments from global bifurcation theory used in Dancer’s original
work.
Submitted: July 28, 2007. Accepted: November 8, 2007. 相似文献
((P)) |
8.
Lei Fu 《Mathematische Zeitschrift》2009,262(2):449-472
Let k be a finite field of characteristic p, l a prime number different from p, a nontrivial additive character, and a character on . Then ψ defines an Artin-Schreier sheaf on the affine line , and χ defines a Kummer sheaf on the n-dimensional torus . Let be a Laurent polynomial. It defines a k-morphism . In this paper, we calculate the weights of under some non-degeneracy conditions on f. Our results can be used to estimate sums of the form
where are multiplicative characters, is a nontrivial additive character, and f
1 , . . . , f
m
, f are Laurent polynomials.
The research is supported by the NSFC (10525107). 相似文献
9.
In this paper we investigate vector-valued parabolic initial boundary value problems , subject to general boundary conditions in domains G in with compact C
2m
-boundary. The top-order coefficients of are assumed to be continuous. We characterize optimal L
p
-L
q
-regularity for the solution of such problems in terms of the data. We also prove that the normal ellipticity condition on
and the Lopatinskii–Shapiro condition on are necessary for these L
p
-L
q
-estimates. As a byproduct of the techniques being introduced we obtain new trace and extension results for Sobolev spaces
of mixed order and a characterization of Triebel-Lizorkin spaces by boundary data.
相似文献
10.
Michele Bolognesi 《Mathematische Zeitschrift》2009,261(1):149-168
Let C be a genus 2 curve and the moduli space of semi-stable rank 2 vector bundles on C with trivial determinant. In Bolognesi (Adv Geom 7(1):113–144, 2007) we described the parameter space of non stable extension
classes of the canonical sheaf ω of C by ω−1. In this paper, we study the classifying rational map that sends an extension class to the corresponding rank two vector bundle. Moreover, we prove that, if we blow up along a certain cubic surface S and at the point p corresponding to the bundle , then the induced morphism defines a conic bundle that degenerates on the blow up (at p) of the Kummer surface naturally contained in . Furthermore we construct the -bundle that contains the conic bundle and we discuss the stability and deformations of one of its components. 相似文献
11.
Let denote the set of simultaneously - approximable points in and denote the set of multiplicatively ψ-approximable points in . Let be a manifold in . The aim is to develop a metric theory for the sets and analogous to the classical theory in which is simply . In this note, we mainly restrict our attention to the case that is a planar curve . A complete Hausdorff dimension theory is established for the sets and . A divergent Khintchine type result is obtained for ; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on of is full. Furthermore, in the case that is a rational quadric the convergent Khintchine type result is obtained for both types of approximation. Our results for
naturally generalize the dimension and Lebesgue measure statements of Beresnevich et al. (Mem AMS, 179 (846), 1–91 (2006)). Moreover, within the multiplicative framework, our results for constitute the first of their type.
The research of Victor V. Beresnevich was supported by an EPSRC Grant R90727/01. Sanju L. Velani is a Royal Society University
Research Fellow.
For Iona and Ayesha on No. 3. 相似文献
12.
Michael Struwe 《Mathematische Zeitschrift》2007,256(2):397-424
For concentrating solutions weakly in H
2(Ω) to the equation on a domain with Navier boundary conditions the concentration energy is shown to be strictly quantized in multiples of the number . 相似文献
13.
Alexander Prestel 《manuscripta mathematica》2007,123(1):95-103
Let K be an algebraically closed field with a valuation ring or a real closed field with a convex valuation ring . We show that the projection of a basic (see “Introduction”) subset of to K
n
is again basic. 相似文献
14.
Jens Habermann 《Mathematische Zeitschrift》2008,258(2):427-462
For weak solutions of higher order systems of the type , for all , with variable growth exponent p : Ω → (1,∞) we prove that if with , then . We should note that we prove this implication both in the non-degenerate (μ > 0) and in the degenerate case (μ = 0). 相似文献
15.
Euisung Park 《Mathematische Zeitschrift》2007,256(3):685-697
In this article we study nondegenerate projective curves of degree d which are not arithmetically Cohen-Macaulay. Note that for a rational normal curve and a point . Our main result is about the relation between the geometric properties of X and the position of P with respect to . We show that the graded Betti numbers of X are uniquely determined by the rank of P with respect to . In particular, X satisfies property N
2,p
if and only if . Therefore property N
2,p
of X is controlled by and conversely can be read off from the minimal free resolution of X. This result provides a non-linearly normal example for which the converse to Theorem 1.1 in (Eisenbud et al., Compositio
Math 141:1460–1478, 2005) holds. Also our result implies that for nondegenerate projective curves of degree d which are not arithmetically Cohen–Macaulay, there are exactly distinct Betti tables. 相似文献
16.
Céline Roucairol 《manuscripta mathematica》2007,124(3):299-318
We compute formal invariants associated with the cohomology sheaves of the direct image of holonomic -modules of exponential type. We also prove that every formal -modules is isomorphic, after a ramification, to a germ of formalized direct image of analytic -module of exponential type. 相似文献
17.
Stefan Gille 《manuscripta mathematica》2006,121(4):437-450
Let
be an Azumaya algebra over a locally noetherian scheme X. We describe in this work quasi-coherent
-bimodules which are injective in the category of sheaves of left
-modules 相似文献
18.
Let be a convex function and be its Legendre tranform. It is proved that if is invariant by changes of signs, then . This is a functional version of the inverse Santaló inequality for unconditional convex bodies due to J. Saint Raymond.
The proof involves a general result on increasing functions on together with a functional form of Lozanovskii’s lemma. In the last section, we prove that for some c > 0, one has always . This generalizes a result of B. Klartag and V. Milman.
相似文献
19.
Joshua A. Cole 《Archive for Mathematical Logic》2008,46(7-8):649-664
Let be the lattice of degrees of non-empty subsets of 2
ω
under Medvedev reducibility. Binns and Simpson proved that FD(ω), the free distributive lattice on countably many generators, is lattice-embeddable below any non-zero element in . Cenzer and Hinman proved that is dense, by adapting the Sacks Preservation and Sacks Coding Strategies used in the proof of the density of the c.e. Turing
degrees. With a construction that is a modification of the one by Cenzer and Hinman, we improve on the result of Binns and
Simpson by showing that for any , we can lattice embed FD(ω) into strictly between and . We also note that, in contrast to the infinite injury in the proof of the Sacks Density Theorem, in our proof all injury
is finite, and that this is also true for the proof of Cenzer and Hinman, if a straightforward simplification is made.
Thanks to my adviser Peter Cholak for his guidance in my research. I also wish to thank the anonymous referee for helpful
comments and suggestions. My research was partially supported by NSF grants DMS-0245167 and RTG-0353748 and a Schmitt Fellowship
at the University of Notre Dame. 相似文献
20.
Javier Pérez Alvarez 《Mathematische Zeitschrift》2009,262(1):17-26
We shall call quantum states of a principal bundle π : P → M with structure group a semi-simple Lie group G, the elements of certain space of sections of the adjoint bundle , associated to the G-bundle of connections . An inner product of sections of is defined for which is a Hilbert space such that the Gauge group gau(P) of the given bundle represents in a family of self-adjoint operators. This work crystallizes some heuristic considerations,
on the unitary representations of Gauge algebras, of Garcia in the already a classical article (J. Differ. Geom. 12, 209–227, 1977). 相似文献