Tate Conjecture for Drinfeld Modules in Equal Characteristic

نویسنده

  • O. Watson
چکیده

We prove that the ring of endomorphisms of the ℘-divisible group of a Drinfeld module of characteristic ℘ is canonically isomorphic to the ring of endomorphisms of the underlying Drinfeld module, completed in the ℘–adic topology. This completes the proof of the Tate Conjectures in the Drinfeld module setting.

برای دانلود رایگان 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

The Sato-tate Law for Drinfeld Modules

We prove an analogue of the Sato-Tate conjecture for Drinfeld modules. Using ideas of Drinfeld, J.-K. Yu showed that Drinfeld modules satisfy some Sato-Tate law, but did not describe the actual law. More precisely, for a Drinfeld module φ defined over a field L, he constructs a continuous representation ρ∞ : WL → D× of the Weil group of L into a certain division algebra, which encodes the Sato-...

متن کامل

The Tate-voloch Conjecture for Drinfeld Modules

We study the v-adic distance from the torsion of a Drinfeld module to an affine variety.

متن کامل

The Erdös and Halberstam Theorems for Drinfeld modules of any rank

Let Fq be the finite field with q elements, A := Fq[T ] and F := Fq(T ). Let φ be a Drinfeld A-module over F with trivial endomorphism ring. We prove analogues of the Erdös and Halberstam Theorems for φ. If φ has rank ≥ 3, we assume the validity of the Mumford-Tate Conjecture for φ. 1

متن کامل

Monodromy Groups associated to Non-Isotrivial Drinfeld Modules in Generic Characteristic

Let φ be a non-isotrivial family of Drinfeld A-modules of rank r in generic characteristic with a suitable level structure over a connected smooth algebraic variety X. Suppose that the endomorphism ring of φ is equal to A. Then we show that the closure of the analytic fundamental group of X in SLr(A f F ) is open, where A f F denotes the ring of finite adèles of the quotient field F of A. From ...

متن کامل

Diophantine Geometry of the Torsion of a Drinfeld Module

We prove an analogue of the Manin-Mumford conjecture for Drinfeld modules of generic characteristic.

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004