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1.
D. Caro 《Inventiones Mathematicae》2007,170(3):507-539
Résumé Soient un anneau de valuation discrète complet d’inégales caractéristiques, de corps résiduel parfait k, un -schéma formel propre et lisse, T un diviseur de la fibre spéciale P de , U l’ouvert de P complémentaire de T, Y un sous-k-schéma fermé lisse de U. Nous prouvons que la catégorie des F-isocristaux surconvergents sur Y est équivalente à celle des F-isocristaux surcohérents sur Y (voir [Car, 6.2.1 et 6.4.3.a)]). Plus généralement, nous établissons par recollement une telle équivalence pour tout k-schéma séparé lisse Y. Nous vérifions de plus que les F-complexes de -modules à cohomologie bornée et -surcohérente se dévissent en F-isocristaux surconvergents. 相似文献
2.
In the study of the asymptotic behaviour of solutions of differential-difference equations the
-spectrum has been useful, where
and
implies Fourier transform
, with
given
, φ∈L
∞(ℝ,X), X a Banach space,
(half)line. Here we study
and related concepts, give relations between them, especially
weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =
; also
= Beurling spectrum of “φ modulo
” (Chill-Fasangova). If
satisfies a Loomis type condition (L
U
), then
countable and
uniformly continuous ∈U are shown to imply
; here (L
U
) usually means
, indefinite integral Pf of f in U imply Pf in
(the Bohl-Bohr theorem for
= almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes
, ℳ
m
U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with
in some
we show
. With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral
integro-differential-difference systems. Also many examples and special cases are discussed. 相似文献
3.
Let be the kernel of the natural map Out(Fn)→GLn(ℤ). We use combinatorial Morse theory to prove that has an Eilenberg–MacLane space which is (2n-4)-dimensional and that is not finitely generated (n≥3). In particular, this shows that the cohomological dimension of is equal to 2n-4 and recovers the result of Krstić–McCool that is not finitely presented. We also give a new proof of the fact, due to Magnus, that is finitely generated. 相似文献
4.
Let be a field and q be a nonzero element of that is not a root of unity. We give a criterion for 〈0〉 to be a primitive ideal of the algebra of quantum matrices. Next, we describe all height one primes of ; these two problems are actually interlinked since it turns out that 〈0〉 is a primitive ideal of whenever has only finitely many height one primes. Finally, we compute the automorphism group of in the case where m ≠ n. In order to do this, we first study the action of this group on the prime spectrum of . Then, by using the preferred basis of and PBW bases, we prove that the automorphism group of is isomorphic to the torus when m ≠ n and (m,n) ≠ (1, 3),(3, 1).
This research was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme
and by Leverhulme Research Interchange Grant F/00158/X. 相似文献
5.
Sorin Popa 《Inventiones Mathematicae》2007,170(2):243-295
We prove that if a countable discrete group Γ is w-rigid, i.e. it contains an infinite normal subgroup H with the relative property (T) (e.g. , or Γ=H×H’ with H an infinite Kazhdan group and H’ arbitrary), and is a closed subgroup of the group of unitaries of a finite separable von Neumann algebra (e.g. countable discrete, or separable compact), then any -valued measurable cocycle for a measure preserving action of Γ on a probability space (X,μ) which is weak mixing on H and s-malleable (e.g. the Bernoulli action ) is cohomologous to a group morphism of Γ into . We use the case discrete of this result to prove that if in addition Γ has no non-trivial finite normal subgroups then any orbit equivalence
between and a free ergodic measure preserving action of a countable group Λ is implemented by a conjugacy of the actions, with respect
to some group isomorphism Γ≃Λ. 相似文献
6.
Tomoyuki Arakawa 《Inventiones Mathematicae》2007,169(2):219-320
We study the representation theory of the -algebra associated with a simple Lie algebra at level k. We show that the “-” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any
level k∈ℂ. Moreover, we show that the character of each irreducible highest weight representation of is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra of . As a consequence we complete (for the “-” reduction) the proof of the conjecture of E. Frenkel, V. Kac and M. Wakimoto on
the existence and the construction of the modular invariant representations of -algebras.
Mathematics Subject Classification (1991) 17B68, 81R10 相似文献
7.
A. Gerlo 《Applied Categorical Structures》2008,16(4):479-493
In a topological construct endowed with a proper -factorization system and a concrete functor , we study -compactness and -Hausdorff separation, where is a class of “closed morphisms” in the sense of Clementino et al. (A functional approach to general topology. In: Categorical
Foundations. Encyclopedia of Mathematics and Its Applications, vol. 97, pp. 103–163. Cambridge University Press, Cambridge,
2004), determined by Λ. In particular, we point out under which conditions on Λ, the notion of -compactness of an object of coincides with 0-compactness of the image in Prap. Our results will be illustrated by some examples: except for some well-known ones, like b-compactness of a topological space, we also capture some compactness notions that were not considered before in the literature.
In particular, we obtain a generalization of b-compactness to the setting of approach spaces. This notion is shown to play an important role in the study of uniformizability.
The author is research assistant at the Fund of Scientific Research Vlaanderen (FWO). 相似文献
8.
Quillen’s algebraic K-theory is reconstructed via Voevodsky’s algebraic cobordism. More precisely, for a ground field k the algebraic cobordism P1-spectrum MGL of Voevodsky is considered as a commutative P1-ring spectrum. Setting we regard the bigraded theory MGL
p,q
as just a graded theory. There is a unique ring morphism which sends the class [X]MGL of a smooth projective k-variety X to the Euler characteristic of the structure sheaf . Our main result states that there is a canonical grade preserving isomorphism of ring cohomology theories
on the category in the sense of [6], where K*(X
on
Z) is Thomason–Trobaugh K-theory and K′
* is Quillen’s K′-theory. In particular, the left hand side is a ring cohomology theory. Moreover both theories are oriented in the sense of
[6] and ϕ respects the orientations. The result is an algebraic version of a theorem due to Conner and Floyd. That theorem
reconstructs complex K-theory via complex cobordism [1]. 相似文献
9.
Martin Kassabov 《Inventiones Mathematicae》2007,170(2):327-354
We construct explicit generating sets S
n
and of the alternating and the symmetric groups, which turn the Cayley graphs and into a family of bounded degree expanders for all n. 相似文献
10.
Frédéric Bayart Pamela Gorkin Sophie Grivaux Raymond Mortini 《Arkiv f?r Matematik》2009,47(2):205-229
We give several characterizations of those sequences of holomorphic self-maps {φ
n
}
n≥1 of the unit disk for which there exists a function F in the unit ball of H
∞ such that the orbit {F∘φ
n
:n∈ℕ} is locally uniformly dense in . Such a function F is said to be a -universal function. One of our conditions is stated in terms of the hyperbolic derivatives of the functions φ
n
. As a consequence we will see that if φ
n
is the nth iterate of a map φ of into , then {φ
n
}
n≥1 admits a -universal function if and only if φ is a parabolic or hyperbolic automorphism of . We show that whenever there exists a -universal function, then this function can be chosen to be a Blaschke product. Further, if there is a -universal function, we show that there exist uniformly closed subspaces consisting entirely of universal functions. 相似文献
11.
Emanuele Delucchi 《Journal of Algebraic Combinatorics》2007,26(4):477-494
Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice
(Proc. Internat. Sympos., 1971, pp. 101–115) and of its subposet of the G-symmetric partitions
which was recently introduced by Hultman (, 2006), together with the complex of G-symmetric phylogenetic trees
. Hultman shows that the complexes
and
are homotopy equivalent and Cohen–Macaulay, and determines the rank of their top homology.
An application of the theory of building sets and nested set complexes by Feichtner and Kozlov (Selecta Math. (N.S.)
10, 37–60, 2004) shows that in fact
is subdivided by the order complex of
. We introduce the complex of Dowling trees
and prove that it is subdivided by the order complex of
. Application of a theorem of Feichtner and Sturmfels (Port. Math. (N.S.)
62, 437–468, 2005) shows that, as a simplicial complex,
is in fact isomorphic to the Bergman complex of the associated Dowling geometry.
Topologically, we prove that
is obtained from
by successive coning over certain subcomplexes. It is well known that
is shellable, and of the same dimension as
. We explicitly and independently calculate how many homology spheres are added in passing from
to
. Comparison with work of Gottlieb and Wachs (Adv. Appl. Math.
24(4), 301–336, 2000) shows that
is intimely related to the representation theory of the top homology of
.
Research partially supported by the Swiss National Science Foundation, project PP002-106403/1. 相似文献
12.
In this paper we establish results on the existence of nontangential limits for weighted
-harmonic functions in the weighted Sobolev space
, for some q>1 and w in the Muckenhoupt A
q
class, where
is the unit ball in
. These results generalize the ones in Sect. 3 of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996, where the weight was identically equal to one. Weighted
-harmonic functions are weak solutions of the partial differential equation
where
for some fixed q∈(1,∞), where 0<α≤β<∞, and w(x) is a q-admissible weight as in Chap. 1 of Heinonen et al., Nonlinear Potential Theory, 2006.
Later, we apply these results to improve on results of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996 and Martio and Srebro, Math. Scand. 85, 49–70, 1999 on the existence of radial limits for bounded quasiregular mappings in the unit ball of
with some growth restriction on their multiplicity function.
相似文献
13.
Andrzej Komisarski 《Journal of Theoretical Probability》2008,21(4):812-823
For a probability space (Ω,ℱ,P) and two sub-σ-fields
we consider two natural distances:
and
. We investigate basic properties of these distances. In particular we show that if a distance (ρ or
) from ℬ to
is small then there exists Z∈ℱ with small P(Z), such that for every B∈ℬ there exists
such that B∖Z and A∖Z differ by a set of probability zero. This improves results of Neveu (Ann. Math. Stat. 43(4):1369–1371, [1972]), Jajte and Paszkiewicz (Probab. Math. Stat. 19(1):181–201, [1999]).
相似文献
14.
Jeroen Demeyer 《Inventiones Mathematicae》2007,170(3):655-670
We construct a Diophantine interpretation of over . Using this together with a previous result that every recursively enumerable (r.e.) relation over is Diophantine over , we will prove that every r.e. relation over is Diophantine over . We will also look at recursive infinite base fields , algebraic over . It turns out that the Diophantine relations over are exactly the relations which are r.e. for every recursive presentation. 相似文献
15.
We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example,
the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of : an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating
the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2. 相似文献
16.
Sascha Orlik 《Inventiones Mathematicae》2008,172(3):585-656
Let be Drinfeld’s upper half space over a finite extension K of ℚ
p
. We construct for every GL
d+1-equivariant vector bundle on ℙ
d
K
, a GL
d+1(K)-equivariant filtration by closed subspaces on the K-Fréchet . This gives rise by duality to a filtration by locally analytic GL
d+1(K)-representations on the strong dual . The graded pieces of this filtration are locally analytic induced representations from locally algebraic ones with respect
to maximal parabolic subgroups. This paper generalizes the cases of the canonical bundle due to Schneider and Teitelbaum [ST1]
and that of the structure sheaf by Pohlkamp [P]. 相似文献
17.
Vladimir Markovic 《Inventiones Mathematicae》2007,168(3):523-566
In this paper, we show that the mapping class group of a closed surface can not be geometrically realized as a group of homeomorphisms
of that surface. More precisely, let denote the standard projection of the group of homeomorphisms to the mapping class group of a closed surface M of genus g>5. We show that there is no homomorphism , such that is the identity. This answers a question by Thurston (see [11]).
Mathematics Subject Classification (2000) Primary 20H10, 37F30 相似文献
18.
Given a set of points
and ε>0, we propose and analyze an algorithm for the problem of computing a (1+ε)-approximation to the minimum-volume axis-aligned ellipsoid enclosing
. We establish that our algorithm is polynomial for fixed ε. In addition, the algorithm returns a small core set
, whose size is independent of the number of points m, with the property that the minimum-volume axis-aligned ellipsoid enclosing
is a good approximation of the minimum-volume axis-aligned ellipsoid enclosing
. Our computational results indicate that the algorithm exhibits significantly better performance than the theoretical worst-case
complexity estimate.
This work was supported in part by the National Science Foundation through CAREER Grants CCF-0643593 and DMI-0237415. 相似文献
19.
Ursula Hamenstädt 《Inventiones Mathematicae》2009,175(3):545-609
We construct a geometric model for the mapping class group of a non-exceptional oriented surface S of genus g with k punctures and use it to show that the action of on the compact metrizable Hausdorff space of complete geodesic laminations for S is topologically amenable. As a consequence, the Novikov higher signature conjecture holds for every subgroup of . 相似文献
20.
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