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Dynamical degrees of self-maps on abelian varieties

编辑:wfy 时间:2019年05月31日 访问次数:193

报告题目: Dynamical degrees of self-maps on abelian varieties

报告人:Fei Hu (英属哥伦比亚大学)

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)