
Contents
-
-
-
-
-
-
-
-
-
-
7.1 Neron-Tate Height 7.1 Neron-Tate Height
-
7.1.1 Neron-Tate height on abelian varieties 7.1.1 Neron-Tate height on abelian varieties
-
7.1.2 Neron-Tate height on curves 7.1.2 Neron-Tate height on curves
-
7.1.3 Intersection theory on arithmetic surfaces 7.1.3 Intersection theory on arithmetic surfaces
-
7.1.4 Arithmetic Hodge index theorem 7.1.4 Arithmetic Hodge index theorem
-
7.1.5 Admissible arithmetic divisors 7.1.5 Admissible arithmetic divisors
-
7.1.6 Admissible extension 7.1.6 Admissible extension
-
7.1.7 Decomposition of the pairing 7.1.7 Decomposition of the pairing
-
-
7.2 Decomposition of the Height Series 7.2 Decomposition of the Height Series
-
7.2.1 Arithmetic model of the Shimura curve 7.2.1 Arithmetic model of the Shimura curve
-
7.2.2 Decomposition of the kernel function 7.2.2 Decomposition of the kernel function
-
-
7.3 Vanishing of the Contribution of the Hodge Classes 7.3 Vanishing of the Contribution of the Hodge Classes
-
7.3.1 Vanishing of the degree of the generating series 7.3.1 Vanishing of the degree of the generating series
-
7.3.2 Integral models of Hecke operators 7.3.2 Integral models of Hecke operators
-
7.3.3 Vanishing of the third term 7.3.3 Vanishing of the third term
-
-
7.4 The Goal of the Next chapter 7.4 The Goal of the Next chapter
-
7.4.1 Dierence of the kernel functions 7.4.1 Dierence of the kernel functions
-
7.4.2 Main result on local computations of the next chapter 7.4.2 Main result on local computations of the next chapter
-
7.4.3 Completion of the proof 7.4.3 Completion of the proof
-
7.4.4 Rough idea of our proof of Theorem 7.8 7.4.4 Rough idea of our proof of Theorem 7.8
-
-
-
-
-
Cite
Abstract
This chapter describes the decomposition of the geometric kernel. It considers the assumptions on the Schwartz function and decomposes the height series into local heights using arithmetic models. The intersections with the Hodge bundles are zero, and a decomposition to a sum of local heights by standard results in Arakelov theory is achieved. The chapter proceeds by reviewing the definition of the Néeron–Tate height and shows how to compute it by the arithmetic Hodge index theorem. When there is no horizontal self-intersection, the height pairing automatically decomposes to a summation of local pairings. The chapter proves that the contribution of the Hodge bundles in the height series is zero. It also compares two kernel functions and states the computational result. It concludes by deducing the kernel identity.
Sign in
Personal account
- Sign in with email/username & password
- Get email alerts
- Save searches
- Purchase content
- Activate your purchase/trial code
- Add your ORCID iD
Purchase
Our books are available by subscription or purchase to libraries and institutions.
Purchasing informationMonth: | Total Views: |
---|---|
August 2024 | 1 |
Get help with access
Institutional access
Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:
IP based access
Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.
Sign in through your institution
Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.
If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.
Sign in with a library card
Enter your library card number to sign in. If you cannot sign in, please contact your librarian.
Society Members
Society member access to a journal is achieved in one of the following ways:
Sign in through society site
Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:
If you do not have a society account or have forgotten your username or password, please contact your society.
Sign in using a personal account
Some societies use Oxford Academic personal accounts to provide access to their members. See below.
Personal account
A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.
Some societies use Oxford Academic personal accounts to provide access to their members.
Viewing your signed in accounts
Click the account icon in the top right to:
Signed in but can't access content
Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.
Institutional account management
For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.