171 research outputs found
Connectivity and a Problem of Formal Geometry
Let be a product of weighted
projective spaces, and let be the diagonal of . We prove
an algebraization result for formal-rational functions on certain closed
subvarieties of along the intersection .Comment: 9 pages, to appear in the Proceedings volume "Experimental and
Theoretical Methods in Algebra, Geometry and Topology", series Springer
Proceedings in Mathematics & Statistic
Remarks on the structure constants of the Verlinde algebra associated to
The structure constants of the Verlinde
algebra as functions of either vanish or can be expressed after a change
of variable as the weight function of an irreducible representation of .
We give a similar formula in the case.Comment: 5 pages, AmsTeX, 1 figure available on reques
Formal properties in small codimension
In this note we extend connectedness results to formal properties of inverse images under proper maps of Schubert varieties and of the diagonal in products of projective rational homogeneous spaces
Automorphisms of moduli spaces of vector bundles over a curve
Let X be an irreducible smooth complex projective curve of genus g at least
4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank
r and fixed determinant \Lambda, of degree d. We give a new proof of the fact
that the automorphism group of M(r,\Lambda) is generated by automorphisms of
the curve X, tensorization with suitable line bundles, and, if r divides 2d,
also dualization of vector bundles.Comment: 12 page
Relational network-service clustering analysis with set evidences
Network administrators are faced with a large amount of network data that they need to sift through to analyze user behaviors and detect anomalies. Through a network monitoring tool, we obtained TCP and UDP connection records together with additional information of the associated users and software in an enterprise network. Instead of using traditional payload inspection techniques, we propose a method that clusters such network traffic data by using relations between entities so that it can be analyzed for frequent behaviors and anomalies. Relational methods like Markov Logic Networks is able to avoid the feature extraction stage and directly handle multi-relation situations. We extend the common pairwise representation in relational models by adopting set evidence to build a better objective for the network service clustering problem. The automatic clustering process helps the administrator filter out normal traffic in shorter time and get an abstract overview of opening transport layer ports in the whole network, which is beneficial for assessing network security risks. Experimental results on synthetic and real datasets suggest that our method is able to discover underlying services and anomalies (malware or abused ports) with good interpretations. © 2010 ACM
On a Conjecture of Rapoport and Zink
In their book Rapoport and Zink constructed rigid analytic period spaces
for Fontaine's filtered isocrystals, and period morphisms from PEL
moduli spaces of -divisible groups to some of these period spaces. They
conjectured the existence of an \'etale bijective morphism of
rigid analytic spaces and of a universal local system of -vector spaces on
. For Hodge-Tate weights and we construct in this article an
intrinsic Berkovich open subspace of and the universal local
system on . We conjecture that the rigid-analytic space associated with
is the maximal possible , and that is connected. We give
evidence for these conjectures and we show that for those period spaces
possessing PEL period morphisms, equals the image of the period morphism.
Then our local system is the rational Tate module of the universal
-divisible group and enjoys additional functoriality properties. We show
that only in exceptional cases equals all of and when the
Shimura group is we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will
appear in Inventiones Mathematica
Regulator constants and the parity conjecture
The p-parity conjecture for twists of elliptic curves relates multiplicities
of Artin representations in p-infinity Selmer groups to root numbers. In this
paper we prove this conjecture for a class of such twists. For example, if E/Q
is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p
extension, then the p-parity conjecture holds for twists of E by all orthogonal
Artin representations of Gal(K^\infty/Q). We also give analogous results when
K/Q is non-abelian, the base field is not Q and E is replaced by an abelian
variety. The heart of the paper is a study of relations between permutation
representations of finite groups, their "regulator constants", and
compatibility between local root numbers and local Tamagawa numbers of abelian
varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat
Twenty-five years of two-dimensional rational conformal field theory
In this article we try to give a condensed panoramic view of the development
of two-dimensional rational conformal field theory in the last twenty-five
years.Comment: A review for the 50th anniversary of the Journal of Mathematical
Physics. Some references added, typos correcte
The Tate conjecture for K3 surfaces over finite fields
Artin's conjecture states that supersingular K3 surfaces over finite fields
have Picard number 22. In this paper, we prove Artin's conjecture over fields
of characteristic p>3. This implies Tate's conjecture for K3 surfaces over
finite fields of characteristic p>3. Our results also yield the Tate conjecture
for divisors on certain holomorphic symplectic varieties over finite fields,
with some restrictions on the characteristic. As a consequence, we prove the
Tate conjecture for cycles of codimension 2 on cubic fourfolds over finite
fields of characteristic p>3.Comment: 20 pages, minor changes. Theorem 4 is stated in greater generality,
but proofs don't change. Comments still welcom
Uniformizing the Stacks of Abelian Sheaves
Elliptic sheaves (which are related to Drinfeld modules) were introduced by
Drinfeld and further studied by Laumon--Rapoport--Stuhler and others. They can
be viewed as function field analogues of elliptic curves and hence are objects
"of dimension 1". Their higher dimensional generalisations are called abelian
sheaves. In the analogy between function fields and number fields, abelian
sheaves are counterparts of abelian varieties. In this article we study the
moduli spaces of abelian sheaves and prove that they are algebraic stacks. We
further transfer results of Cerednik--Drinfeld and Rapoport--Zink on the
uniformization of Shimura varieties to the setting of abelian sheaves. Actually
the analogy of the Cerednik--Drinfeld uniformization is nothing but the
uniformization of the moduli schemes of Drinfeld modules by the Drinfeld upper
half space. Our results generalise this uniformization. The proof closely
follows the ideas of Rapoport--Zink. In particular, analogies of -divisible
groups play an important role. As a crucial intermediate step we prove that in
a family of abelian sheaves with good reduction at infinity, the set of points
where the abelian sheaf is uniformizable in the sense of Anderson, is formally
closed.Comment: Final version, appears in "Number Fields and Function Fields - Two
Parallel Worlds", Papers from the 4th Conference held on Texel Island, April
2004, edited by G. van der Geer, B. Moonen, R. Schoo
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