Degrees of the elliptic Teichmuller lift

[摘要] The purpose of this paper is to find upper bounds for the degrees, or equivalently, for the order of the poles at O, of the coordinate functions of the elliptic Teichmuller lift of an ordinary elliptic curve over a perfect field of characteristic p. We prove the following bounds: ord(0)(x(n)) greater than or equal to - (n + 2)p(n) + np(n-1), ord(0)(y(n)) greater than or equal to - (n + 3)p(n) + np(n-1) Also, we prove that the bound for x, is not the exact order if, and only if, p divides (n + 1), and the bound for y(n) is not the exact order if, and only if, p divides (n + 1)(n + 2)/2. Finally, we give an algorithm to compute the reduction modulo p(3) of the canonical lift for p not equal 2,3. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-08-01

[关键词] elliptic curves;canonical liftings;elliptic Teichmaller life