Mathematics – Algebraic Geometry
Scientific paper
2008-06-27
J. Reine Angew. Math. 642 (2010), 157-196
Mathematics
Algebraic Geometry
33 pages, 1 figure
Scientific paper
10.1515/CRELLE.2010.040
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.
No associations
LandOfFree
Trees of definable sets over the p-adics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Trees of definable sets over the p-adics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trees of definable sets over the p-adics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-692672