An Estimate of the Growth of Cohomology with Coefficients

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Authors

  • Chaitanya Ambi
     ,IN

DOI:

https://doi.org/10.18311/jims/2021/27831

Keywords:

Group Cohomology, algebraic Groups, Adelic locally symmetric space, sheaf cohomology
Primary 20G10, Secondary 57R19

Abstract

For a connected reductive algebraic group over an arbitrary number eld, we consider a nite dimensional algebraic, irreducible representation of the group of its real points. Each adelic locally symmetric space corresponding to a level structure constructed using the group has an associated sheaf induced by this representation. The purpose of this note is to estimate the rate of growth of the total dimension of the pertinent cohomology with coecients as either of the level structure or the associated sheaf varies. We obtain an upper bound on this total dimension. We also obtain a lower bound under certain topological conditions. Both the bounds are consistent with several classical dimension formulae as well as other known results.

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Published

2021-06-14

How to Cite

Ambi, C. (2021). An Estimate of the Growth of Cohomology with Coefficients. The Journal of the Indian Mathematical Society, 88(3-4), 187–200. https://doi.org/10.18311/jims/2021/27831

Issue

Volume 88, Issue 3-4, July-December 2021

Section

Articles

License

Copyright (c) 2021 Chaitanya Ambi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2021-05-19
Accepted 2021-05-19
Published 2021-06-14

 

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