Eichler shimura isomorphism
WebThe Eichler-Shimura isomorphism establishes a bijection between the space of modular forms and certain cohomology groups with coefficients in a space of poly-nomials. More precisely, let k≥ 2 be an integer and let Γ ⊆ SL2(Z) be a congruence subgroup, then we have the following isomorphism of Hecke modules WebLecture 18 : Eichler-Shimura Theory Instructor: Henri Darmon Notes written by: Dylan Attwell-Duval Recall We saw last time that the modular curves Y 1(N) =Q are a ne curves whose points are in correspondence with elliptic curves and level structure, up to Q-isomorphism (Q-isomorphism when N>3). See J.Milne’s online notes for details. Hecke ...
Eichler shimura isomorphism
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Webthe elements appearing on the right hand side of the Eichler{Shimura isomorphism are (classical) modular, respectively cusp forms of weight k C2. There is a more arithmetic version of the above theorem, which we will also call a classical Eichler{Shimura isomorphism. Namely let us consider now the modular curve WebThe Shimura-Taniyama-Weil con- jecture, which after [16]can be called a theorem (in most cases), says that the inverse Mellin transform of LQ(E,s) which is defined as is a weight 2 cusp form for the congruence subgroup r o ( N )of SL2(Z): where N is a positive integer called the conductor of E. ... Then the rnap giuen by: for a + O j E HP,(aJ E ...
Webthe Eichler{Shimura isomorphism is basically a piece of complex Hodge theory, and involves sheaves, cohomology, etc., that have complex coe cients, whereas to detect congruences mod p, one has to use cohomology with integral, or perhaps mod p, WebMar 30, 2024 · By the Eichler-Shimura isomorphism, we actually give a sharp bound of the second cohomology of a hyperbolic three manifold (Bianchi manifold) with local system arising from the representation ∼k⊗∼—k of SL2 (C). I will explain how a p-adic algebraic method is used for deriving our result. Date March 30, 2024 Affiliation Princeton …
WebLecture 4 Geometric modular forms, Kodaira{Spencer isomorphism, Eichler{Shimura isomorphism Lecture 5 Compacti cation of modular curves Lecture 6 Galois representations associated to modular forms Lecture 7 Siegel modular varieties, Shimura varieties of PEL type Lecture 8 General theory of Shimura varieties Lecture 9 Dual BGG … WebA theorem of Eichler and Shimura says that the space of cusp forms with complex coefficients appears as a direct summand of the cohomology of the compactified modular curve. Ohta has proven an analog of this theorem for the space of ordinary p-adic cusp forms with integral coefficients.
WebNov 29, 2024 · The Eichler Shimura isomorphism computes the cohomology of the symmetric powers of this local system. Note that it is normally phrased as a statement about group cohomology of Γ := S L 2 ( Z) with coefficients in its natural polynomial representations, these two statements are equivalent according to the analytic …
WebNov 1, 2024 · With this in mind, the Eichler–Shimura isomorphism can be obtained comparing deRham and singular cohomology, noticing that the singular cohomology of the open modular curve is given by the group cohomology . The aim of this paper is to omit this geometric interpretation and to provide a new group cohomological interpretation. halfords executive teamWebThe Eichler-Shimura Isomorphism. We give a description of quaternionic au-tomorphic forms as sections of certain locally free sheaves on M(C) and show that QM( k) ⊕QM( ) is the Hodge decomposition of a certain local system on M(C). In fact there is a way to make sense of this even over the completion at some prime of bungalow bay garden city scWeb6. I have seen a couple of questions related to the Eichler-Shimura Isomorphism, but almost all of them have to do with hodge theory (things I am unfamiliar with) and seem, to me, different/unrelated. Let S k ( Γ) denote the space of modular cusp forms of level Γ ⊂ S L 2 ( Z) and let V k − 2 ⊂ C [ X, Y] be the homogenous polynomials of ... halfords exhaust repair pasteWebMar 2, 2013 · We give a new proof of Ohta's Lambda-adic Eichler-Shimura isomorphism using p-adic Hodge theory and the results of Bloch-Kato and Hyodo on p-adic etale cohomology. This paper contains many mistakes, and would require substantial revisions to make it suitable for publication. halfords exhaustWebTheorem 1.2 (Eichler-Shimura) . There is a Hecke-equivariant isomorphism S k S k E k ()! H i( ;Sym k 2 (C 2)) where acts on C 2 via ,! GL 2 (C ). Here S k denotes the space of anti-holomorphic cusp forms, which in this case is actually isomorphic to S k (). We will explain what \Hecke-equivariant" means later on in the talk. 2. Modular Symbols halfords exhaust mountWebIn this chapter we describe the Eichler-Shimura theory already mentioned in the preceding chapter. Skip to main content . Advertisement. Search. Go to cart. Search SpringerLink ... The Eichler-Shimura Isomorphism on SL 2 (Z). In: Introduction to Modular Forms. Grundlehren der mathematischen Wissenschaften, vol 222. Springer, Berlin, Heidelberg ... halfords exhaust strapWebFrom this, we deduce a Q-de Rham Eichler-Shimura isomorphism, and a definition of the period matrix of a Hecke eigenspace. Before stating the main results, it may be instructive to review the familiar case of an elliptic curve E over Q with equation y2 = 4x3 − ux− v. The de Rham Date: December 21, 2024. 1991 Mathematics Subject ... halfords exmouth devon