2024 Eichler shimura isomorphism

Eichler shimura isomorphism

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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 … 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 ( …

The p-adic Eichler-Shimura isomorphism UCI Mathematics

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 ... WebThe Eichler-Shimura isomorphism theorem asserts that r− (resp. r+) is an isomorphism onto W− (resp. W+ 0 ⊆ W +, the codimension 1 subspace not containing zk−2 − 1). Therefore W 0 ⊆ W, the corresponding codimension 1 subspace, represents two copies of S k. Concerning W 0 and zk−2 −1, Kohnen and Zagier ask (see p. 201 of [18 ... pilot callsign ideas

OVERCONVERGENT EICHLER-SHIMURA ISOMORPHISMS …

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 ... 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 … 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 … pingdom free speed test

Eichler–Shimura isomorphism and group cohomology on

[PDF] Concentration of closed geodesics in the homology 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 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. pilot call signs in top gunWebJan 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 … pingdom offers

"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 … " - Eichler shimura isomorphism

Eichler shimura isomorphism

EICHLER-SHIMURA THEORY FOR MOCK MODULAR FORMS

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 ...

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http://math.bu.edu/INDIVIDUAL/ghs/papers/EichlerShimura.pdf 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 ...

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. WebApr 19, 2024 · I am now trying to understand the so-called Eichler-Shimura isomorphism. For the references, I am now reading the book "Introduction to the Arithmetic Theory of Automorphic Functions" and the paper "Sur les integrales attachees aux formes automorphes" by G. Shimura.

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. http://math.columbia.edu/~mundy/cag.html

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.

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 ... pingdom monitor processhttp://math.bu.edu/people/ghs/papers/EichlerShimura.pdf pingdom monitoring toolWebThe 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 pingdom healthWeb1 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. pilot canford heathWebThe 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 pilot cap goggles istockWebFrom 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 ... pingdom powershellWebtheory. One variant of the classical theory is the Eichler-Shimura isomorphism between spaces of modular forms and singular cohomology. It deals with a variation of Hodge-structure over a non-compact base of dimension one. In this paper we give the p-adic analogue. One of our results is the following: pilot candy