Matches in SemOpenAlex for { <https://semopenalex.org/work/W2969609293> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W2969609293 abstract "In this thesis we accomplish four main results related to Jacobians of curves. Firstly, we find a large number of hyperelliptic curves of genus 2, 3 and 4 whose Jacobians have torsion points of large order. The genus 2 case is particularly well-studied in the literature, and we provide a new example of a geometrically simple Jacobian of a genus 2 curve with a point of order 25, an order which was not previously known. For geometrically simple Jacobians of curves of genus 3 and 4, we extend the known orders of points, increasing the largest known order in both cases to 91 and 88, respectively. Secondly, we find an explicit embedding of the Kummer variety of a genus 3 superelliptic curve into projective space. This is a natural extension of the embeddings that are already known for the Kummer varieties of hyperelliptic curves of genus 2 and 3. Thirdly, we classify the genus 2 curves whose Jacobians admit a (4,4)- isogeny. We find an infinite family of genus 2 curves for which the elements of the kernel of the (4,4)-isogeny are defined over the ground field, and make partial progress on classifying the genus 2 curves with this property. We also extend Flynn’s example of a genus 2 curve whose Jacobian admits a (5, 5)-isogeny to infinitely many geometrically nonisomorphic curves. Finally, we extend Schaefer’s algorithm for computing the Selmer group of a Jacobian to carry out a (4, 4)-descent on Jacobians of curves that admit a (4, 4)-isogeny." @default.
- W2969609293 created "2019-08-29" @default.
- W2969609293 creator A5067409721 @default.
- W2969609293 date "2018-01-01" @default.
- W2969609293 modified "2023-09-23" @default.
- W2969609293 title "Descent methods and torsion on Jacobians of higher genus curves" @default.
- W2969609293 hasPublicationYear "2018" @default.
- W2969609293 type Work @default.
- W2969609293 sameAs 2969609293 @default.
- W2969609293 citedByCount "0" @default.
- W2969609293 crossrefType "dissertation" @default.
- W2969609293 hasAuthorship W2969609293A5067409721 @default.
- W2969609293 hasConcept C11074058 @default.
- W2969609293 hasConcept C136119220 @default.
- W2969609293 hasConcept C157369684 @default.
- W2969609293 hasConcept C179603306 @default.
- W2969609293 hasConcept C200331156 @default.
- W2969609293 hasConcept C202444582 @default.
- W2969609293 hasConcept C2779765290 @default.
- W2969609293 hasConcept C28826006 @default.
- W2969609293 hasConcept C33923547 @default.
- W2969609293 hasConcept C86803240 @default.
- W2969609293 hasConcept C90856448 @default.
- W2969609293 hasConceptScore W2969609293C11074058 @default.
- W2969609293 hasConceptScore W2969609293C136119220 @default.
- W2969609293 hasConceptScore W2969609293C157369684 @default.
- W2969609293 hasConceptScore W2969609293C179603306 @default.
- W2969609293 hasConceptScore W2969609293C200331156 @default.
- W2969609293 hasConceptScore W2969609293C202444582 @default.
- W2969609293 hasConceptScore W2969609293C2779765290 @default.
- W2969609293 hasConceptScore W2969609293C28826006 @default.
- W2969609293 hasConceptScore W2969609293C33923547 @default.
- W2969609293 hasConceptScore W2969609293C86803240 @default.
- W2969609293 hasConceptScore W2969609293C90856448 @default.
- W2969609293 hasLocation W29696092931 @default.
- W2969609293 hasOpenAccess W2969609293 @default.
- W2969609293 hasPrimaryLocation W29696092931 @default.
- W2969609293 hasRelatedWork W1496030291 @default.
- W2969609293 hasRelatedWork W1572184567 @default.
- W2969609293 hasRelatedWork W1596013679 @default.
- W2969609293 hasRelatedWork W1953880282 @default.
- W2969609293 hasRelatedWork W2013081204 @default.
- W2969609293 hasRelatedWork W2052980309 @default.
- W2969609293 hasRelatedWork W2092828923 @default.
- W2969609293 hasRelatedWork W2150435208 @default.
- W2969609293 hasRelatedWork W2403559215 @default.
- W2969609293 hasRelatedWork W2570007677 @default.
- W2969609293 hasRelatedWork W2618014470 @default.
- W2969609293 hasRelatedWork W26827147 @default.
- W2969609293 hasRelatedWork W2756037186 @default.
- W2969609293 hasRelatedWork W2901879081 @default.
- W2969609293 hasRelatedWork W2949436203 @default.
- W2969609293 hasRelatedWork W2951504030 @default.
- W2969609293 hasRelatedWork W2971148876 @default.
- W2969609293 hasRelatedWork W2996016660 @default.
- W2969609293 hasRelatedWork W2999743071 @default.
- W2969609293 hasRelatedWork W3132515178 @default.
- W2969609293 isParatext "false" @default.
- W2969609293 isRetracted "false" @default.
- W2969609293 magId "2969609293" @default.
- W2969609293 workType "dissertation" @default.