507 research outputs found
Bailey flows and Bose-Fermi identities for the conformal coset models
We use the recently established higher-level Bailey lemma and Bose-Fermi
polynomial identities for the minimal models to demonstrate the
existence of a Bailey flow from to the coset models
where is a
positive integer and is fractional, and to obtain Bose-Fermi identities
for these models. The fermionic side of these identities is expressed in terms
of the fractional-level Cartan matrix introduced in the study of .
Relations between Bailey and renormalization group flow are discussed.Comment: 28 pages, AMS-Latex, two references adde
Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)
In this paper, we formulate the geometric Bogomolov conjecture for abelian
varieties, and give some partial answers to it. In fact, we insist in a main
theorem that under some degeneracy condition, a closed subvariety of an abelian
variety does not have a dense subset of small points if it is a non-special
subvariety. The key of the proof is the study of the minimal dimension of the
components of a canonical measure on the tropicalization of the closed
subvariety. Then we can apply the tropical version of equidistribution theory
due to Gubler. This article includes an appendix by Walter Gubler. He shows
that the minimal dimension of the components of a canonical measure is equal to
the dimension of the abelian part of the subvariety. We can apply this result
to make a further contribution to the geometric Bogomolov conjecture.Comment: 30 page
The Theorem of Jentzsch--Szeg\H{o} on an analytic curve. Application to the irreducibility of truncations of power series
The theorem of Jentzsch--Szeg\H{o} describes the limit measure of a sequence
of discrete measures associated to the zeroes of a sequence of polynomials in
one variable. Following the presentation of this result by Andrievskii and
Blatt in their book, we extend this theorem to compact Riemann surfaces, then
to analytic curves over an ultrametric field. The particular case of the
projective line over an ultrametric field gives as corollaries information
about the irreducibility of the truncations of a power series in one variable.Comment: 16 pages; the application to irreducibility and the final example
have been correcte
Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations
We resolve the local semistable reduction problem for overconvergent
F-isocrystals at monomial valuations (Abhyankar valuations of height 1 and
residue transcendence degree 0). We first introduce a higher-dimensional
analogue of the generic radius of convergence for a p-adic differential module,
which obeys a convexity property. We then combine this convexity property with
a form of the p-adic local monodromy theorem for so-called fake annuli.Comment: 36 pages; v3: refereed version; adds appendix with two example
Event Stream Processing with Multiple Threads
Current runtime verification tools seldom make use of multi-threading to
speed up the evaluation of a property on a large event trace. In this paper, we
present an extension to the BeepBeep 3 event stream engine that allows the use
of multiple threads during the evaluation of a query. Various parallelization
strategies are presented and described on simple examples. The implementation
of these strategies is then evaluated empirically on a sample of problems.
Compared to the previous, single-threaded version of the BeepBeep engine, the
allocation of just a few threads to specific portions of a query provides
dramatic improvement in terms of running time
Rogers-Szego polynomials and Hall-Littlewood symmetric functions
We use Rogers-Szego polynomials to unify some well-known identities for
Hall-Littlewood symmetric functions due to Macdonald and Kawanaka.Comment: 18 page
Motivic Serre invariants, ramification, and the analytic Milnor fiber
We show how formal and rigid geometry can be used in the theory of complex
singularities, and in particular in the study of the Milnor fibration and the
motivic zeta function. We introduce the so-called analytic Milnor fiber
associated to the germ of a morphism f from a smooth complex algebraic variety
X to the affine line. This analytic Milnor fiber is a smooth rigid variety over
the field of Laurent series C((t)). Its etale cohomology coincides with the
singular cohomology of the classical topological Milnor fiber of f; the
monodromy transformation is given by the Galois action. Moreover, the points on
the analytic Milnor fiber are closely related to the motivic zeta function of
f, and the arc space of X.
We show how the motivic zeta function can be recovered as some kind of Weil
zeta function of the formal completion of X along the special fiber of f, and
we establish a corresponding Grothendieck trace formula, which relates, in
particular, the rational points on the analytic Milnor fiber over finite
extensions of C((t)), to the Galois action on its etale cohomology.
The general observation is that the arithmetic properties of the analytic
Milnor fiber reflect the structure of the singularity of the germ f.Comment: Some minor errors corrected. The original publication is available at
http://www.springerlink.co
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