Diophantine approximation and local distribution of rational points - TIB AV-Portal

Diophantine approximation and local distribution of rational points

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Institut Fourier

Huang, Zhizhong

Formale Metadaten

Titel

Diophantine approximation and local distribution of rational points

Serientitel

Summer School 2017 - Arakelov Geometry and diophantine applications

Anzahl der Teile

43

Autor

Huang, Zhizhong

Lizenz

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Identifikatoren

10.5446/63252 (DOI)

Herausgeber

Institut Fourier

Erscheinungsjahr

Sprache

Inhaltliche Metadaten

Fachgebiet

Genre

Abstract

We show how to use the recent work of D. McKinnon and M. Roth on generalizations of Diophantine approximation to algebraic varieties to formulate a local version of the Batyrev-Manin principle on the distribution of rational points. We present several toric varieties for which the result is known.

Serie

Summer School 2017 - Arakelov Geometry and diophantine applications36 / 43

1

55:15

Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (Part 1)

2

59:43

Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (Part 4)

3

1:33:45

Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (Part 2)

4

1:31:53

Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (Part 3)

5

1:31:50

Arithmetic Intersection (Part 1)

6

1:10:09

Arithmetic Intersection (Part 2)

7

1:26:13

Arithmetic Intersection (Part 3)

8

1:24:43

Arithmetic Intersection (Part 4)

9

1:02:21

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 1)

10

1:30:57

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 2)

11

1:03:34

Théorème de Hilbert-Samuel arithmétique (Part 2)

12

1:01:34

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 3)

13

1:33:12

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 4)

14

54:53

The height of CM points on orthogonal Shimura varieties and Colmez conjecture (Part 5)

15

1:31:05

Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part 1)

16

1:24:56

Arakelov theory on Shimura varieties (Part 2)

17

1:26:53

Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part 2)

18

1:21:09

Arakelov theory on Shimura varieties (Part 1)

19

1:00:50

Théorème de Hilbert-Samuel arithmétique (Part 1)

20

1:31:06

Automorphic forms and arithmetic intersections (Part 2)

21

46:14

Automorphic forms and arithmetic intersections (Part 3)

22

1:26:47

Minima et pentes des espaces adéliques rigides (Part 1)

23

1:31:00

Minima et pentes des espaces adéliques rigides (Part 2)

24

1:33:49

Some problems of arithmetic origin in complex dynamics and geometry (Part 1)

25

1:30:23

Minima et pentes des espaces adéliques rigides (Part 3)

26

1:00:10

Sieving rational points on algebraic varieties

27

1:32:37

Some problems of arithmetic origin in complex dynamics and geometry (Part 3)

28

1:29:51

Slopes and distribution of points (Part 1)

29

1:02:42

Slopes and distribution of points (Part 2)

30

55:57

Slopes and distribution of points (Part 3)

31

1:28:47

Slopes and distribution of points (Part 4)

32

1:31:01

Some problems of arithmetic origin in complex dynamics and geometry (Part 2)

33

1:01:14

An analytic class number type formula for PSL2(Z)

34

1:04:38

Quantitative aspects of rational points on algebraic varieties (Part 1)

35

1:00:15

On the arithmetic degree of Shimura curves

36

1:02:27

Diophantine approximation and local distribution of rational points

37

1:03:58

Quantitative aspects of rational points on algebraic varieties (Part 2)

38

1:24:44

Quantitative aspects of rational points on algebraic varieties (Part 3)

39

1:29:59

Quantitative aspects of rational points on algebraic varieties (Part 4)

40

1:31:49

Arithmetic Intersection (Part 1)

41

1:10:09

Arithmetic Intersection (Part 2)

42

1:26:13

Arithmetic Intersection (Part 3)

43

1:03:01

Exceptional splitting of reductions of abelian surfaces with real multiplication

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