Related papers: Sous-vari\'et\'es de codimension $2$ d'une vari\'e…
We extend to the general codimension a lower bound for the essential minimum on abelian varieties found in a previous work, under a conjecture about ordinary primes in abelian varieties. This lower bound is the best expected, ``up to an…
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Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.
This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.
There is a mathematical error in the first version of this paper. A new corrected version will be posted when the error is fixed, possibly with a modified title.
Given an abelian variety $A$ of dimension $g$ over a number field $K$, and a prime $\ell$, the $\ell^n$-torsion points of $A$ give rise to a representation $\rho_{A, \ell^n} : \gal(\bar{K} / K) \to \gl_{2g}(\zz/\ell^n\zz)$. In particular,…
We study asymptotic behaviour of graded codimensions of Lie superalgebra $b(2)$. We prove that graded PI-exponent exists and is equal to $3+2\sqrt 3$.
We prove a few new properties of a Hankel transform related to limited series expansions. This preprint superseed the preprint math.CO/0303221 of the first author.
We review the results of our previous publication [Phys. Rev. D63, 116001 (2001); hep-ph/0012226] in the light of recent calculations and comments.
This article has been withdrawn due to a mistake which is explained in version 2.
withdrawn by the author due to double submission in arXiv:1102.4271 .
This short survey, which was written to accompany a minicourse at the BIRS conference "Topology in dimension 4.5", concerns invariants of knotted $2$-spheres in $S^4$, also known as $2$-knots. It covers invariants extracted from the…
Recently, R\'emond stated a very general conjecture on lower bounds of a normalized height on either an abelian variety or a power of the multiplicative group. In this note, we extend a particular case of this conjecture to split…
These notes discuss in an informal manner the construction and some properties of 1- and 2-gerbes. They are mainly based on the author's previous work in this area, which is reviewed here, and to some extent improved upon. The main emphasis…
We give a new lower bound for the essential minimum of subvarieties of abelian varieties with small codimension, under a conjecture about ordinary primes in abelian varieties. This lower bound is already known in the toric case since the…
We prove a version of adelic descent for continuous localizing invariants.
We describe derivations and subalgebras of codimensions 1 of conservative algebras of small dimensions.
I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
In this version we have corrected some minor errors in the tables, corrected typos, and added a reference. We have also updated our comparison with earlier workers. Figures are now included as uuencoded compressed tar files.