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Given an endomorphism of a projective variety, by intersecting the graph and the diagonal varieties we can determine the set of periodic points. In an effort to determine the periodic points of a given minimal period, we follow a construction similar to cyclotomic polynomials. The resulting zero-cycle is called a dynatomic cycle and the points in its support are called formal periodic points. This article gives a proof of the effectivity of dynatomic cycles for morphisms of projective varieties using methods from deformation theory.
Given a generic polynomial $f(x)$, the generalized dynatomic polynomial $Phi_{f,c,d}(x)$ vanishes at precisely those $alpha$ such that $f^c(alpha)$ has period exactly $d$ under iteration of $f(x)$. We show that the shifted dynatomic polynomials $Phi_
We determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define boundary components of special divisors and prove that the generating
The aim of this article is to prove, using complex Abel-Jacobi maps, that the subgroup generated by Heegner cycles associated with a fixed imaginary quadratic field in the Griffiths group of a Kuga-Sato variety over a modular curve has infinite rank.
We consider cycles on a 3-dimensional Shimura varieties attached to a unitary group, defined over extensions of a CM field $E$, which appear in the context of the conjectures of Gan, Gross, and Prasad cite{gan-gross-prasad}. We establish a vertical d
Let $k$ be a number field, let $X$ be a Kummer variety over $k$, and let $delta$ be an odd integer. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational points over finite extensions of $k$ to that of zero-cycles over $k$ f