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Estimation of the Dimension of Cuspidal and Total Cohomology

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dc.contributor.advisor RAGHURAM, A. en_US
dc.contributor.author AMBI, CHAITANYA en_US
dc.date.accessioned 2019-09-23T07:03:39Z
dc.date.available 2019-09-23T07:03:39Z
dc.date.issued 2019-09 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/4091
dc.description Ph.D. Thesis en_US
dc.description.abstract We consider the Weil restriction of a connected reductive algebraic group over a number field to the rational numbers. For a level structure in the group of its adelic points, we form an adelic locally symmetric space. A finite-dimensional, algebraic, irreducible representation of the group of real points of the Weil restriction induces an associated sheaf on this space. Raghuram and Bhagwat found certain necessary conditions for non-vanishing of the cuspidal part of the respective sheaf cohomology in case of the general linear group under some additional assumptions on the number field and the weight of the representation. Motivated by this, we estimate the growth rate of cuspidal cohomology with varying level structure as well as weight in case of automorphic induction from GL(1) over imaginary quadratic fields to GL(2) over the rationals and also that of symmetric square transfer from GL(2) to GL(3); both over the rationals. We also present bounds on the dimension of the total sheaf cohomology which apply to an arbitrary connected reductive algebraic group with varying level structure or weight. The bounds thus obtained are consistent with the classical dimension formulae as well as several known results. en_US
dc.description.sponsorship NBHM en_US
dc.language.iso en en_US
dc.subject 2019 en_US
dc.subject Langlands Transfer en_US
dc.subject Cuspidal Cohomology en_US
dc.title Estimation of the Dimension of Cuspidal and Total Cohomology en_US
dc.type Thesis en_US
dc.publisher.department Dept. of Mathematics en_US
dc.type.degree Ph.D en_US
dc.contributor.department Dept. of Mathematics en_US
dc.contributor.registration 20143346 en_US


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  • PhD THESES [603]
    Thesis submitted to IISER Pune in partial fulfilment of the requirements for the degree of Doctor of Philosophy

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