Eichler shimura isomorphism
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 … 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 …
Eichler shimura isomorphism
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Web19 rows · Seminar on the Cohomology of Arithmetic Groups. In the fall of 2024, I organized a seminar on the cohomology of arithmetic groups. Topics included: the Eichler-Shimura isomorphism, Matsushima's formula, Eisenstein classes, coherent cohomology, and Venkatesh's conjectures. Web6. 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 ...
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 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 ...
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, 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 …
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 ...
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 ... poa healthcare wisconsinWebThe 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)_); poa healthcare texasWebThe 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 poa housesIn mathematics, Eichler cohomology (also called parabolic cohomology or cuspidal cohomology) is a cohomology theory for Fuchsian groups, introduced by Eichler (1957), that is a variation of group cohomology analogous to the image of the cohomology with compact support in the ordinary cohomology group. The Eichler–Shimura isomorphism, introduced by Eichler for complex cohomology and by Shimura (1959) for real cohomology, is an isomorphism between an Eichler … poa hearingWebNov 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. poa healthcare meaningWebMar 20, 2013 · The second goal of this paper is the interpolation of the Eichler-Shimura decomposition (6.0.1). The H 0 of the overconvergent ES maps was previously constructed by Andreatta-Iovita-Stevens in [AIS15] poa homeownersWebNov 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 … poa heart