منابع مشابه
On Tate Local Duality
Let Fq be a finite field, and let g be its absolute Galois group. Hence g ∼= Ẑ, topologically generated by the Frobenius automorphism. Let A be a topological g−module, i.e. for each a ∈ A there is a positive integer n such that Frobn a = a (for us A will be either an elliptic curve or some torsion group). Thus the group A is the union of its subgroups Agn , the latter being g/gn-module, where g...
متن کاملOn a Theorem of Tate
A far-reaching generalization of this result is the Tate conjecture, asserting algebraicity of Tate classes, i.e., `-adic cohomology classes conformally invariant under the action of Frobenius. In this note we provide an alternative condition for the existence of surjective morphisms between abelian varieties and, more generally, Tate classes in the cohomology of products of arbitrary algebraic...
متن کاملComputing Tate Pairing on Smartcards
In this paper, we present the results of computing the Tate pairing using a supersingular elliptic curve defined over a prime field. The aim of this work is to demonstrate the feasibility of the primitives of identity based cryptosystem for application in embedded processors such as a smartcard. The most computationally intensive operation in an Identity Based Protocol is the calculation of a p...
متن کاملRecent Progress on the Tate Conjecture
We survey the history of the Tate conjecture on algebraic cycles. The conjecture is closely related with other big problems in arithmetic and algebraic geometry, including the Hodge and Birch–Swinnerton-Dyer conjectures. We conclude by discussing the recent proof of the Tate conjecture for K3 surfaces over finite fields.
متن کاملRemarks on the Tate Conjecture for beginners
The pair of conjectures of Tate, called T1 and T2 below, are of great importance. They provide analogues of two other famous conjectures, namely the Hodge Conjecture, which is a prediction in Complex Geometry, and the Birch and Swinnerton-Dyer Conjecture, which is a centrepiece of Number theory. This dual aspect is what makes the Tate conjecture central and also very difficult to solve in gener...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Iowa Review
سال: 1996
ISSN: 0021-065X,2330-0361
DOI: 10.17077/0021-065x.4561