منابع مشابه
The Manin constant
The Manin constant of an elliptic curve is an invariant that arises in connection with the conjecture of Birch and Swinnerton-Dyer. One conjectures that this constant is 1; it is known to be an integer. After surveying what is known about the Manin constant, we establish a new sufficient condition that ensures that the Manin constant is an odd integer. Next, we generalize the notion of the Mani...
متن کاملThe Manin Constant, Congruence Primes, and the Modular Degree
We obtain relations between the modular degree and congruence modulus of elliptic curves, and answer a question raised in a paper of Frey and Müller about whether or not the congruence number and modular degree of elliptic curves are always equal; they are not, but we give a conjectural relation between them. We also prove results and make conjectures about Manin constants of quotients of J1(N)...
متن کاملThe Manin Constant of Elliptic Curves over Function Fields
We study the p-adic valuation of the values of normalised Hecke eigenforms attached to non-isotrivial elliptic curves defined over function fields of transcendence degree one over finite fields of characteristic p. We derive upper bounds on the smallest attained valuation in terms of the minimal discriminant under a certain assumption on the function field and provide examples to show that our ...
متن کاملThe Brauer–Manin obstruction
Let X be a smooth, geometrically irreducible variety over a field k. Recall that the defining property of an Azumaya algebra A is that, for any field K containing k and any point P ∈ X(K), we can evaluate A at P to get a central simple algebra A(P ) over K. In particular, suppose that k is a number field. Then, for each place v of k, we can evaluate A at points of X(kv) to get central simple al...
متن کاملBeyond the Manin Obstruction
Br(X)/Br0(X)×X(Ak) → Q/Z. We shall call this the Brauer–Manin pairing. Let us define X(Ak) Br as “the right kernel” of this pairing, that is, the subset of points of X(Ak) orthogonal to all elements of Br(X). Manin made an important observation that by the global reciprocity law the image ofX(k) under the diagonal embedding X(k) →֒ X(Ak) is contained in X(Ak) . A variety X such that X(Ak) 6= ∅ w...
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: Pure and Applied Mathematics Quarterly
سال: 2006
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2006.v2.n2.a11