منابع مشابه
Isogenous to a Product of Curves
A smooth algebraic surface S is isogenous to a product, not of mixed type, if there exist two smooth curves C, F and a finite group G, acting faithfully on both C and F and freely on their product, so that S = (C × F )/G. In this paper we classify the surfaces of general type with pg = q = 1 which are isogenous to an unmixed product, assuming that the group G is abelian. It turns out that they ...
متن کاملOn standardized models of isogenous elliptic curves
Let E, E′ be isogenous elliptic curves over Q given by standardized Weierstrass models. We show that (in the obvious notation) a1 = a1, a ′ 2 = a2, a ′ 3 = a3 and, moreover, that there are integers t, w such that a4 = a4 − 5t and a6 = a6 − b2t − 7w, where b2 = a1 + 4a2.
متن کاملModular Towers of Noncongruence Curves
This proposal extends much work done during the last funding period. Two topics, however, which have separate goals, have brief summaries in x10. Together they form documentation of the results that came from the funding period of NSF GRANT #9622928. 1. An outline of the main problems of this proposal Let G be a nite group. Call a conjugacy class C a p 0-class if its elements have order prime t...
متن کاملFamilies of Explicitly Isogenous Jacobians of Variable-separated Curves
We construct six infinite series of families of pairs of curves (X, Y ) of arbitrarily high genus, defined over number fields, together with an explicit isogeny JX → JY splitting multiplication by 2, 3, or 4. The families are derived from Cassou–Noguès and Couveignes’ explicit classification of pairs (f, g) of polynomials such that f(x1)− g(x2) is reducible.
متن کاملTowers of Curves and Rational Distance Sets
A rational (resp. integral) distance set is a subset S of the plane R such that for all s, t ∈ S, the distance between s and t is a rational number (resp. is an integer). Huff [4] considered rational distance sets S of the following form: given distinct a, b ∈ Q∗, S contains the four points (0,±a) and (0,±b) on the y-axis, plus points (x, 0) on the x-axis, for some x ∈ Q∗. Such a point (x, 0) m...
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: Compositio Mathematica
سال: 2015
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x15007423