Dynamical degrees of self-maps on abelian varieties
报告题目： Dynamical degrees of self-maps on abelian varieties
时间：2019年6月3日（周一）下午4:00-5:00
地点：工商楼200-9
摘要： Let $X$ be a smooth projective variety defined over an algebraically closed field of arbitrary characteristic, and $f/colon X /to X$ a surjective morphism. The $i$-th cohomological dynamical degree $/chi_i(f)$ of $f$ is defined as the spectral radius of the pullback $f^*$ on the /'etale cohomology group $H^i_{et}(X, /bQ_/ell)$ and the $k$-th numerical dynamical degree $/lambda_k(f)$ as the spectral radius of the pullback $f^*$ on the vector space $N^k(X)_/bR$ of real algebraic cycles of codimension $k$ modulo numerical equivalence. Truong conjectured that $/chi_{2k}(f) = /lambda_k(f)$ for any $1 /le k /le /dim X$. When the ground field is the complex number field, the equality follows from the positivity property inside the de Rham cohomology of the ambient complex manifold $X(/bC)$. We prove this conjecture in the case of abelian varieties. The proof relies on a new result on the eigenvalues of self-maps of abelian varieties in prime characteristic, which is of independent interest.
联系人：叶和溪老师（yehexi@zju.edu.cn)