Eichler shimura isomorphism

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August undefined, 2024

WebLet us review the classical Eichler-Shimura isomorphism on modular curves. Fix a prime p ≥3, an integer N ≥3 such that (p,N) = 1 and let Γ := Γ1(N)∩Γ0(p) ⊆SL2(Z). the universal semi-abelian scheme and ω := ω E/X = e∗(Ω1 E/X) the invertible sheaf on X of invariant 1-diﬀerentials, where e : X →E is the zero section. We have ... 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,

EICHLER-SHIMURA ISOMORPHISM AND GROUP …

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The Eichler-Shimura Isomorphism on SL2(Z) SpringerLink

WebShimura curves. Section 2 is devoted to the classical Eichler-Shimura isomorphism in the context of Shimura curves. In section 3 we introduce the spaces of overconvergent modular symbols. Section 4 is the technical part of this work, we de ne modular sheaves on Faltings’ sites and we construct the map from overconvergent WebEichler-Shimura isomorphism. Introduction The classical Eichler-Shimura isomorphism describes the space of weight k2N modular symbols in terms of elliptic modular forms of weight k+ 2. Faltings in [12] gave an arithmetic version of this isomorphism. WebMar 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. auth0 ユーザー情報取得

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Eichler–Shimura isomorphism - Wikipedia

WebTheorem 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 auth0 とはわかりやすくWebappearing on the right hand side of the Eichler-Shimura isomorphism are (classical) modular, respectively cusp forms of weight k+ 2. 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 Xover the p-adic eld Kand for k 0 an integer ... authblk.sty ダウンロード

"WebAug 1, 2024 · The Eichler–Shimura isomorphism states that the space Sk(Γ)is isomorphic to the first (parabolic) cohomology group associated to the Γ-module Rk−1with an appropriate Γ-action. Manin reformulated the Eichler–Shimura isomorphism for the case Γ=SL2(Z)in terms of periods of cusp forms. " - Eichler shimura isomorphism

Eichler shimura isomorphism

WebNov 21, 2024 · The well-known Eichler–Shimura isomorphism (cf. [36], [107]) provides us a correspondence between modular forms for a discrete subgroup $$ \varGamma \subset SL \left(2, {\mathbb{R}}\right) $$ and cohomology classes … 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.

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WebThe 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 WebA0.5 (half) overconvergent Eichler-Shimura isomorphism 123 X(N, p)such that we have H1, Dk ∼= H1 X(N, p)ket K,Dk. In particular H1, Dk has a natural action of the absolute Galois group GK of K. In [3] we have proved a full but imperfect Eichler-Shimura isomorphism theorem for H1, Dk as follows: for every slope h ≥ 0, there is a discrete set ...

WebEichler-Shimura isomorphism and mixed Hodge theory Asked 13 years, 3 months ago Modified 10 years, 6 months ago Viewed 2k times 18 Let Y ( N), N > 2 be the quotient of the upper half-plane by Γ ( N) (which is formed by the elements of S L ( … 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.

Web1 Eichler-Shimura Isomorphism 1.1 Cohomology of Fuchsian Groups LetGbe a group,Rbe a given ring,Mbe aR[G]-module. We define the group cohomology as H∗(G;M) := Ext∗ R[G](R;M); whereRis endowed with the trivialG-action. WebJan 3, 2024 · The Eichler-Shimura isomorphism realizes the automorphic representation generated by an automorphic newform in certain cohomology of an arithmetic group. In this short note, we give a cohomological interpretation of the Eichler-Shimura isomorphism as a connection morphism of certain exact sequence of G …

WebEICHLER-SHIMURA THEORY 3 In fact, this modular curve admits the structure of a smooth projective variety over Q. Establishing this fact will use several ideas. We start with a standard result from algebraic geometry. Let k be a ﬁeld (usually this will be Q). Deﬁnition 2.1. AﬁeldK is a (one-dimensional) function ﬁeld over k if (1) K ∩k ...

WebThe Eichler-Shimura isomorphism establishes a bijection between the space of modular forms and certain cohomology groups with coe cients in a space of poly-nomials. More precisely, let k 2 be an integer and let SL 2(Z) be a congruence subgroup, then we have the following isomorphism of Hecke modules (0.1) M k( ;C) S k( ;C) ’H1( ;V(k)_); authense法律事務所エストコーポレーションWebThe Eichler–Shimura congruence relation and its generalizations to Shimura varieties play a pivotal role in the Langlands program, by identifying a part of the Hasse–Weil zeta function of a modular curve or a more general modular variety, with the product of Mellin transforms of weight 2 modular forms or a product of analogous automorphic L … auth0 認証プロバイダ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 … auth0 認証基盤サービスWebFrom 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 ... authcadトレーニング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 … authense法律事務所関根やばいWebAug 1, 2024 · The Eichler–Shimura isomorphism [10] states that the space S k (Γ) is isomorphic to the first (parabolic) cohomology group associated to the Γ-module R k − 1 with an appropriate Γ-action. Manin [6] reformulated the Eichler–Shimura isomorphism for the case Γ = SL 2 (Z) in terms of periods of cusp forms (see also [5, Chapter 5, Theorem ... auth404 アウトルックWebTHE EICHLER-SHIMURA ISOMORPHISM ASHWIN IYENGAR Contents 1. Introduction 1 2. Modular Symbols 1 3. Cohomology 2 4. Cusp Forms 3 5. Hecke Operators 5 6. Correspondences 5 7. Eisenstein Series 6 References 7 1. Introduction We are studying the cohomology of arithmetic groups. Today, we will describe the case where when G= SL 2, auth areaからの要求ユーザー名