dc.date.accessioned | 2020-07-08T14:22:08Z | |
dc.date.available | 2020-07-08T14:22:08Z | |
dc.date.issued | 2020 | |
dc.identifier | doi:10.17170/kobra-202007081428 | |
dc.identifier.uri | http://hdl.handle.net/123456789/11635 | |
dc.language.iso | eng | eng |
dc.rights | Urheberrechtlich geschützt | |
dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
dc.subject | Drinfeld modules | eng |
dc.subject | iosgeny classes | eng |
dc.subject | isomorphism classes | eng |
dc.subject | endomorphism rings | eng |
dc.subject.ddc | 510 | |
dc.title | Explicit Description Of Isogeny And Isomorphism Classes Of Drinfeld Modules Of Higher Rank Over Finite Fields | eng |
dc.type | Dissertation | |
dcterms.abstract | When jumping from the number fields theory to the function fields theory, one cannot miss the deep analogy between rank 1 Drinfeld modules and the group of root of unity and the analogy between rank 2 Drinfeld modules and elliptic curves. But so far, there is no known structure in number fields theory that is analogous to the Drinfeld modules of higher rank r ≥ 3. In this thesis we investigate the classes of those Drinfeld modules of higher rank r ≥ 3 defined over a finite field L. We describe explicitly the Weil polynomials defining the isogeny classes of rank r Drinfeld modules defined over a finite field L for any rank r ≥ 3, which generalizes what Yu already did for r = 2. We also provide a necessary and sufficient condition for an order O in the endomorphism algebra corresponding to some isogeny classes, to be the endomorphism ring of a Drinfeld module. To complete the classification, we define the notion of fine isomorphy invariants for any rank r Drinfeld module defined over a finite field L and we prove that the fine isomorphy invariants together with the J-invariants describe the L-isomorphism classes of rank r Drinfeld modules defined over the finite field L. | eng |
dcterms.accessRights | open access | |
dcterms.creator | Nkotto Nkung Assong, Sedric | |
dcterms.dateAccepted | 2020-07-01 | |
dcterms.extent | vii, 107 Seiten | |
dc.contributor.corporatename | Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften, Institut für Mathematik | |
dc.contributor.referee | Rück, Hans Georg (Prof. Dr.) | |
dc.subject.swd | Drinfeld-Modul | ger |
dc.subject.swd | Isogenie | ger |
dc.subject.swd | Endomorphismus | ger |
dc.type.version | publishedVersion | |
kup.iskup | false | |