Muutke küpsiste eelistusi

Moduli Spaces and Arithmetic Dynamics [Kõva köide]

  • Formaat: Hardback, 140 pages, kaal: 430 g
  • Sari: CRM Monograph Series
  • Ilmumisaeg: 30-Mar-2012
  • Kirjastus: American Mathematical Society
  • ISBN-10: 0821875825
  • ISBN-13: 9780821875827
Teised raamatud teemal:
Moduli Spaces and Arithmetic DynamicsSuurem pilt
  • Formaat: Hardback, 140 pages, kaal: 430 g
  • Sari: CRM Monograph Series
  • Ilmumisaeg: 30-Mar-2012
  • Kirjastus: American Mathematical Society
  • ISBN-10: 0821875825
  • ISBN-13: 9780821875827
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780821875827.html
Märksõnad:
This monograph studies moduli problems associated to algebraic dynamical systems. It is an expanded version of the notes for a series of lectures delivered at a workshop on Moduli Spaces and the Arithmetic of Dynamical Systems at the Bellairs Research Institute, Barbados, in 2010. The author's goal is to provide an overview, with enough details and pointers to the existing literature, to give the reader an entry into this exciting area of current research. Topics covered include: (1) Construction and properties of dynamical moduli spaces for self-maps of projective space. (2) Dynatomic modular curves for the space of quadratic polynomials. (3) The theory of canonical heights associated to dynamical systems. (4) Special loci in dynamical moduli spaces, in particular the locus of post-critically finite maps. (5) Field of moduli and fields of definition for dynamical systems.

Arvustused

The monograph is an expanded version of Silverman's lecture notes from a workshop held in May 2010, on the topic of moduli spaces of dynamical systems. It is a pleasure to read, as much as it was a pleasure to attend the lectures. Silverman writes well: he explains the mathematics clearly and includes many explicit examples. Best of all, he has peppered the text with leading questions and side remarks, opening doors to hundreds of potential research projects. It will be a useful reference for students and senior researchers alike. ...Every chapter of this monograph offers multiple entries, many conjectural, in the "Silverman dictionary." For anyone already familiar with both the arithmetic theory of elliptic curves and the traditionally analytic results about these dynamical systems, recent results in arithmetic dynamics make the analogies beautifully apparent; with this book, Silverman helps the rest of us to appreciate the similarities." - Laura De Marco, University of Illinois at Chicago

Preface vii
Introduction 1(2)
Chapter 1 Moduli Spaces Associated to Dynamical Systems
3(8)
1.1 Dynamical definitions
3(2)
1.2 Moduli spaces: what they are and why they're useful
5(1)
1.3 Fine moduli spaces and coarse moduli spaces
5(1)
1.4 Parameter spaces for dynamical systems
6(2)
1.5 Moduli spaces for dynamical systems
8(1)
1.6 Level structure and the uniform boundedness conjecture
8(3)
Chapter 2 The Geometry of Dynamical Moduli Spaces
11(34)
2.1 Introduction to geometric invariant theory (GIT)
12(5)
2.2 Tools for computing the stable and semistable loci
17(3)
2.3 Construction of moduli spaces Mnd using GIT
20(4)
2.4 Multipliers and maps on Md
24(6)
2.5 M2 is isomorphic to A2
30(4)
2.6 Uniform bounds for Aut(ø)
34(2)
2.7 Rationality of M1d
36(3)
2.8 Special loci in Mnd
39(6)
Chapter 3 Dynamical Moduli Spaces---Further Topics
45(12)
3.1 An application to good reduction over function fields
45(2)
3.2 Minimal resultants and minimal models
47(3)
3.3 Dynamics on K3 Surfaces
50(3)
3.4 An algebraic characterization of Lattes maps
53(4)
Chapter 4 Dynatomic Polynomials and Dynamical Modular Curves
57(12)
4.1 Dynatomic polynomials
57(2)
4.2 Dynamical modular curves for z2 + c
59(1)
4.3 Irreducibility and genus formulas
60(5)
4.4 Rational points on dynamical modular curves
65(1)
4.5 Other dynamical modular curves
65(4)
Chapter 5 Canonical Heights
69(22)
5.1 Heights and projective space
69(1)
5.2 Dynamical canonical heights
70(3)
5.3 Canonical height zero over function fields
73(3)
5.4 Local heights and Green functions
76(1)
5.5 Specialization theorems
77(4)
5.6 Heights and dominant rational maps
81(2)
5.7 Canonical heights for regular affine automorphisms
83(1)
5.8 Canonical heights for K3 dynamics
84(4)
5.9 Algebraic dynamics and transcendental numbers
88(3)
Chapter 6 Postcritically Finite Maps
91(22)
6.1 Transversality of the PCF locus
92(8)
6.2 The height of a postcritically finite map
100(7)
6.3 The invariant measure and the Lyapunov exponent
107(2)
6.4 Conservative maps
109(1)
6.5 A dynamical Andre-Oort conjecture
110(3)
Chapter 7 Field of Moduli and Field of Definition
113(8)
7.1 Twists, automorphisms, and cohomology
113(3)
7.2 Fields of definition and field of moduli
116(1)
7.3 Tools for determining when FOM = FOD
117(4)
Schedule of Talks at the Bellairs Workshop 121(2)
Glossary 123(4)
Bibliography 127(6)
Index 133
Joseph H. Silverman, Brown University, Providence, RI, USA