Abstract for the seminar talks on 25.04.2008

Prof. Tarlok Shorey (Tata Institute Mumbay)
Irreducibility of some polynomials considered by Schur
Time: 14.15 / Place: HWZ (HG G43)

Schur considered the polynomial a_n x^n/n! + a_{n-1} x^{n-1}/(n-1)! + ... + a_1 x/1! + a_0, where a_i are integers with a_0 and a_n are either 1 or -1, and showed that it is irreducible. We shall consider more general polynomials a_n x^n/(n+a)! +a{n-1} x^{n-1}/(n-1+a)!+ +a_1 x/ (1+a)! + a_0 /a!, where a is not necessarily zero, and give several extensions of Schur's result.

Dr. Aurélien Galateau (Univ. Basel)
The effective Bogomolov conjecture in abelian varieties
Time: 15.45 / Place: HWZ (HG G43)

I will speak about an explicit version of the Bogomolov problem in abelian varieties. Under a conjecture concerning ordinary primes in abelian varieties, I give a lower bound for the essential minimum of subvarieties with small codimension, which is the analog of the bound known in the toric case since the work of Amoroso and David. The key point is a p-adic lemma concerning the formal group of an abelian variety in positive caracteristic. I will finally discuss the diophantine setting and the possible extension to general codimension.