香蕉视频

Title:聽Dynamical degrees of self-maps on abelian varieties.

Abstract:聽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.