2018
DOI: 10.1515/crelle-2017-0052
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Relative dynamical degrees of correspondences over a field of arbitrary characteristic

Abstract: Let {\mathbb{K}} be an algebraically closed field of arbitrary characteristic, X and Y irreducible possibly singular algebraic varieties over {\mathbb{K}}. Let {f:X\vdash X} and {g:Y\vdash Y} be dominant correspondences, and {\pi:X\dashrightarrow Y} a dominant rational map which semi-conjugate f and g, i.e. so that {\pi\circ f=g\circ\pi}. We define relative dynamical degrees {\lambda_{p}(f|\pi)\geq 1} for any {p=0,\dots,\dim(X)-\dim(Y)}. These degrees measure the relative growth of positive algebraic cycles, s… Show more

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Cited by 39 publications
(36 citation statements)
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“…In previous work [26], we have defined (relative) dynamical degrees, for rational maps and more general correspondences, of algebraic varieties (not necessarily smooth or compact) over an arbitrary field, in terms of algebraic cycles modulo numerical equivalences.…”
Section: Algebraicétale Dynamical Systems and Entropymentioning
confidence: 99%
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“…In previous work [26], we have defined (relative) dynamical degrees, for rational maps and more general correspondences, of algebraic varieties (not necessarily smooth or compact) over an arbitrary field, in terms of algebraic cycles modulo numerical equivalences.…”
Section: Algebraicétale Dynamical Systems and Entropymentioning
confidence: 99%
“…In the algebraic setting, over fields K different from C, there is still no definition of cohomological entropy. There are indications [6,12,26] that one should be willing to work with objects such asétale topology -seemingly further away from dynamical systems -in order to come closer to satisfying Gromov -Yomdin 's theorem. In fact, for automorphisms of compact surfaces, the work in [12] relates the quantity in Gromov -Yomdin's theorem to l-adic cohomology, which suggests that we may even need to deal with stranger objects thanétale topology.…”
Section: Algebraicétale Dynamical Systems and Entropymentioning
confidence: 99%
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