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. 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 …
arXiv:1708.00652v2 [math.NT] 22 Dec 2024
In 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 … 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)_); taya kyle wins shooting competition
Overconvergent Eichler-Shimura isomorphisms - BU
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 ... 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. 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 … tayal sons private limited