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Comment on “The economic consequences of Empires (1492-1989)”
Editada en la Fundación Empresa PúblicaPublicad
Trees of definable sets over the p-adics
To a definable subset of Z_p^n (or to a scheme of finite type over Z_p) one
can associate a tree in a natural way. It is known that the corresponding
Poincare series P(X) = \sum_i N_i X^i is rational, where N_i is the number of
nodes of the tree at depth i. This suggests that the trees themselves are far
from arbitrary. We state a conjectural, purely combinatorial description of the
class of possible trees and provide some evidence for it. We verify that any
tree in our class indeed arises from a definable set, and we prove that the
tree of a definable set (or of a scheme) lies in our class in three special
cases: under weak smoothness assumptions, for definable subsets of Z_p^2, and
for one-dimensional sets.Comment: 33 pages, 1 figur
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