Dirichlet motives via modular curves
نویسنده
چکیده
Generalizing ideas of Anderson, Harder has proposed a construction of extensions of motives of Dirichlet-Tate type in sheaf theoretic terms (cf. [Ha] Section 4.2 or the review before Prop. 6.4). Let Mk(−1) be the smooth ladic sheaf on Y1(p) given as k-th symmetric power of the Tate module of the universal elliptic curve over Y1(p). Decomposing a certain l-adic cohomology group with coefficients in Mk under the Hecke-algebra Harder obtains (after extension of scalars to Q(μp)) for each Dirichlet character η mod p with η(−1) = (−1)k an extension of Galois-modules
منابع مشابه
Se p 20 09 Motives for elliptic modular groups
In order to study the arithmetic structure of elliptic modular groups which are the fundamental groups of compactified modular curves with cuspidal base points, these truncated Malcev Lie algebras and their direct sums are considered as elliptic modular motives. Our main result is a new theory of Hecke operators on these motives which gives a congruence relation to the Galois action, and a moti...
متن کاملEmergent Spacetime from Modular Motives
The program of constructing spacetime geometry from string theoretic modular forms is extended to Calabi-Yau varieties of dimensions two, three, and four, as well as higher rank motives. Modular forms on the worldsheet can be constructed from the geometry of spacetime by computing the L-functions associated to omega motives of Calabi-Yau varieties, generated by their holomorphic n−forms via Gal...
متن کاملA Nonvanishing Theorem for Derivatives of Automorphic L-functions with Applications to Elliptic Curves
1. A brief history of nonvanishing theorems. The nonvanishing of a Dirichlet series 2 a(n)n~\ or the existence of a pole, at a particular value of s often has applications to arithmetic. Euler gave the first example of this, showing that the infinitude of the primes follows from the pole of Ç(s) at s = 1. A deep refinement was given by Dirichlet, whose theorem on primes in an arithmetic progres...
متن کاملBeilinson ’ S Theorem on Modular Curves
0. Introduction. The purpose of this chapter is to give a detailed account of the known evidence ([Be1], §5) for Beilinson’s conjecture concerning the values at s = 2 of L-functions of modular forms of weight two. We do not discuss here the results concerning the L-values at other integers s ≥ 2 (for which see [Be2]), nor do we treat the case of the product of two modular curves (also to be fou...
متن کاملMotives and Deligne’s Conjecture
Deligne’s conjecture [Del] asserts that the values of certain L-functions are equal, up to rational multiples, to the determinants of certain period matrices. The conjectures are most easily stated for projective, smooth varieties over number fields. Such a variety has an L-function whose local factors encode Frobenius eigenvalues. The isomorphism between de Rham and Betti cohomologies gives a ...
متن کاملذخیره 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 1997