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. 

clockCreated with Sketch.Date / heure

vendredi 18 octobre 2019
11 h à 12 h

pinCreated with Sketch.Lieu

UQAM - Pavillon Président-Kennedy (PK)
PK-5115
201, avenue du Président-Kennedy
Montréal (QC)

personCreated with Sketch.Renseignements

Mots-clés

Groupes