Weil-etale Cohomology over Local Fields
| dc.contributor.advisor | Ramachandran, Niranjan | en_US |
| dc.contributor.author | Karpuk, David Anton | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2012-07-07T05:56:44Z | |
| dc.date.available | 2012-07-07T05:56:44Z | |
| dc.date.issued | 2012 | en_US |
| dc.description.abstract | In a recent article, Lichtenbaum established the arithmetic utility of the Weil group of a finite field, by demonstrating a connection between certain Euler characteristics in Weil-etale cohomology and special values of zeta functions. In particular, the order of vanishing and leading coefficient of the zeta function of a smooth, projective variety over a finite field have a Weil-etale cohomological interpretation. These results rely on a duality theorem stated in terms of cup-product in Weil-etale cohomology. With Lichtenbaum's paradigm in mind, we establish results for the cohomology of the Weil group of a local field, analogous to, but more general than, results from Galois cohomology. We prove a duality theorem for discrete Weil group modules, which implies the main theorem of Local Class Field Theory. We define Weil- smooth cohomology for varieties over local fields, and prove a duality theorem for the cohomology of G_m on a smooth, proper curve with a rational point. This last theorem is analogous to, and implies, a classical duality theorem for such curves. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1903/12677 | |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | Algebraic Geometry | en_US |
| dc.subject.pquncontrolled | Number Theory | en_US |
| dc.title | Weil-etale Cohomology over Local Fields | en_US |
| dc.type | Dissertation | en_US |
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