The André-Oort conjecture for products of Drinfeld modular curves

نویسنده

  • Florian Breuer
چکیده

Let Z = X1×· · ·×Xn be a product of Drinfeld modular curves. We characterize those algebraic subvarieties X ⊂ Z containing a Zariski-dense set of CM points, i.e. points corresponding to n-tuples of Drinfeld modules with complex multiplication (and suitable level structure). This is a characteristic p analogue of a special case of the André-Oort conjecture.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

O-minimality and the André-Oort conjecture for Cn

We give an unconditional proof of the André-Oort conjecture for arbitrary products of modular curves. We establish two generalizations. The first includes the Manin-Mumford conjecture for arbitrary products of elliptic curves defined over Q as well as Lang’s conjecture for torsion points in powers of the multiplicative group. The second includes the ManinMumford conjecture for abelian varieties...

متن کامل

0 Ju l 2 00 4 CM points on products of Drinfeld modular curves Florian Breuer

Let X be a product of Drinfeld modular curves over a general base ring A of odd characteristic. We classify those subvarieties of X which contain a Zariski-dense subset of CM points. This is an analogue of the André-Oort conjecture. As an application, we construct non-trivial families of higher Heegner points on modular elliptic curves over global function fields.

متن کامل

O-minimality and the André-Oort conjecture for C

We give an unconditional proof of the André-Oort conjecture for arbitrary products of modular curves. We establish two generalizations. The first includes the Manin-Mumford conjecture for arbitrary products of elliptic curves defined over Q as well as Lang’s conjecture for torsion points in powers of the multiplicative group. The second includes the Manin-Mumford conjecture for abelian varietie...

متن کامل

O-minimality as an Approach to the André-oort Conjecture

— Employing a proof technique suggested by Zannier and first successfully implemented by Pila and Zannier to give a reproof of the Manin-Mumford conjecture on algebraic relations on torsion points of an abelian variety, Pila presented an unconditional proof of the André-Oort conjecture when the ambient Shimura variety is a product of modular curves. In subsequent works, these results have been ...

متن کامل

subvarieties of Drinfeld modular varieties Florian

The André-Oort conjecture for Shimura varieties over C states that any subvariety X of a Shimura variety S/C containing a Zariski-dense set of special points must be of Hodge type. For an up-to-date overview of this topic, and of known results, see Rutger Noot’s Bourbaki talk [18]. The most significant result so far is due to Bas Edixhoven and Andrei Yafaev [9], who prove that any subcurve X ⊂ ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003