Date
2020Metadata
Show full item record
Dissertation
Explicit Description Of Isogeny And Isomorphism Classes Of Drinfeld Modules Of Higher Rank Over Finite Fields
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.
Citation
@phdthesis{doi:10.17170/kobra-202007081428,
author={Nkotto Nkung Assong, Sedric},
title={Explicit Description Of Isogeny And Isomorphism Classes Of Drinfeld Modules Of Higher Rank Over Finite Fields},
school={Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften, Institut für Mathematik},
year={2020}
}
0500 Oax
0501 Text $btxt$2rdacontent
0502 Computermedien $bc$2rdacarrier
1100 2020$n2020
1500 1/eng
2050 ##0##http://hdl.handle.net/123456789/11635
3000 Nkotto Nkung Assong, Sedric
4000 Explicit Description Of Isogeny And Isomorphism Classes Of Drinfeld Modules Of Higher Rank Over Finite Fields / Nkotto Nkung Assong, Sedric
4030
4060 Online-Ressource
4085 ##0##=u http://nbn-resolving.de/http://hdl.handle.net/123456789/11635=x R
4204 \$dDissertation
4170
5550 {{Drinfeld-Modul}}
5550 {{Isogenie}}
5550 {{Endomorphismus}}
7136 ##0##http://hdl.handle.net/123456789/11635
<resource xsi:schemaLocation="http://datacite.org/schema/kernel-2.2 http://schema.datacite.org/meta/kernel-2.2/metadata.xsd"> 2020-07-08T14:22:08Z 2020-07-08T14:22:08Z 2020 doi:10.17170/kobra-202007081428 http://hdl.handle.net/123456789/11635 eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Drinfeld modules iosgeny classes isomorphism classes endomorphism rings 510 Explicit Description Of Isogeny And Isomorphism Classes Of Drinfeld Modules Of Higher Rank Over Finite Fields Dissertation 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. open access Nkotto Nkung Assong, Sedric 2020-07-01 vii, 107 Seiten Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften, Institut für Mathematik Rück, Hans Georg (Prof. Dr.) Drinfeld-Modul Isogenie Endomorphismus publishedVersion false </resource>
The following license files are associated with this item:
:Urheberrechtlich geschützt