On cohomology groups attached to towers of algebraic curves
type: Item
instance of: scholarly article
title: On cohomology groups attached to towers of algebraic curves
zbMATH Open document ID: 0820.14014
author: Masami Ohta
published in: Journal of the Mathematical Society of Japan
publication date: 1995-09-17T00:00:00Z
review text: Motivated by a work of \textit{Y. Ihara} [Invent. Math. 86, 427-459 (1986; Zbl 0585.14020)], we develop a ``one-dimensional \(\ell\)-adic cohomology theory'' for ``almost pro-\(\ell\)'' towers of algebraic curves consisting of étale coverings of a fixed base curve. More precisely, we describe the projective limits of (three kinds of) \(\ell\)-adic étale cohomology groups of the members of a given tower in terms of continuous cochain cohomology groups and an analogue of the group of modular symbols. When the base curve is \(\mathbb{P}^ 1 - \{0,1, \infty\}\), we show that our cohomology theory is closely related to Ihara's theory. We also study the cohomology groups of towers of elliptic modular curves, especially in connection with the theory of \(\ell\)-adic representations attached to elliptic cusp forms.
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 469056
zbMATH Keywords: \(\ell\)-adic cohomology theory
zbMATH Keywords: \(\ell\)-adic representations
zbMATH Keywords: towers of algebraic curves
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04510131
OpenAlex ID: W2079097498
DOI: 10.2969/JMSJ/04510131
description: scientific article; zbMATH DE number 469056