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Etale Cohomology and Rationality of L-series of Varieties

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dc.contributor.advisor Nair, Arvind en_US
dc.contributor.author KOPARDE, ABHISHEK en_US
dc.date.accessioned 2022-05-13T12:46:21Z
dc.date.available 2022-05-13T12:46:21Z
dc.date.issued 2022-05
dc.identifier.citation 80 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6942
dc.description.abstract Etale cohomology was introduced by A. Grothendieck and developed by him with the help of M. Artin and J. L. Verdier, to explain A. Weil's insight that for polynomial equations with integer coefficients, the topology of the set of complex solutions should profoundly influence the number of solutions of the equations modulo a prime number. Weil conjectured that the zeta function (introduced by Hasse for curves and by Weil in general) of a smooth projective variety over a finite field $\mathbb{F}_q$, which is a generating function that captures the growth of the number of points defined over $\mathbb{F}_{q^n}$ as $n$ increases, is a rational function, satisfies a certain functional equation and has its zeroes at restricted places. Since \'etale cohomology gives a replacement, for arbitrary schemes, of the cohomology of the space of complex points of a variety, and since it gives a sheaf theory and cohomology theory whose properties closely resemble those arising from the complex topology, it allows for the use of topological ideas over general fields, both in algebraic geometry and in many areas (number theory, representation theory, algebra) where algebraic geometry plays an essential role. en_US
dc.language.iso en en_US
dc.subject Algebraic Geometry en_US
dc.title Etale Cohomology and Rationality of L-series of Varieties en_US
dc.type Thesis en_US
dc.type.degree BS-MS en_US
dc.contributor.department Dept. of Mathematics en_US
dc.contributor.registration 20171169 en_US


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  • MS THESES [1705]
    Thesis submitted to IISER Pune in partial fulfilment of the requirements for the BS-MS Dual Degree Programme/MSc. Programme/MS-Exit Programme

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