Séminaire Cirget: «Dynamical degrees of self-maps on abelian varieties»
Conférencier:Fei Hu, University of Waterloo
Résumé/Abstract: Let $X$ be a smooth projective variety defined over an algebraically closed field, and $f$ a dominant self-correspondence of $X$. There are two natural dynamical invariants associated to this $f$, the $i$-th cohomological dynamical degree $\chi_i(f)$ defined by iterating the pullback action of $f$ on the $i$-th $\ell$-adic cohomology vector space of $X$ and the $k$-th numerical dynamical degree $\lambda_k(f)$ defined by the iterated pullback action of $f$ on the real vector space of numerical equivalence classes of codimension-$k$ cycles.
Truong conjectured that $\chi_{2k}(f) = \lambda_k(f)$ for $k= 1, ..., \dim X$.
I will discuss this conjecture in the case of abelian varieties. Along the way, we also obtain a new result on the eigenvalues of self-maps of abelian varieties in prime characteristic, which is of independent interest.
Date / heure
Lieu
Montréal (QC)