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Computing Ceresa classes of curves
Multi angle
Authors : Srinivasan, Padmavathi (Author of the conference)
CIRM (Publisher )
11G30 - Curves of arbitrary genus or genus $\ne 1$ over global fields [See also 14H25]
11G40 - $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
14C25 - Algebraic cycles
14H25 - Arithmetic ground fields, See also {11Dxx,11G05,14Gxx}
14Q05 - Computational aspects of algebraic curves
CIRM (Publisher )
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Abstract :
The Ceresa class is the image under a cycle class map of a canonical algebraic cycle associated to a curve in its Jacobian. This class vanishes for all hyperelliptic curves, and is known to be non-vanishing for the generic curve of genus at least 3. It is necessary for the Ceresa class to have infinite order for the Galois action on the fundamental group of a curve to have big image. We will present an algorithm for certifying that a curve over a number field has infinite order Ceresa class.
N.B. This is preliminary joint work with Jordan Ellenberg, Adam Logan and Akshay Venkatesh.
Keywords : Ceresa cycle; Ceresa class; nontriviality in the Griffiths group
MSC Codes : N.B. This is preliminary joint work with Jordan Ellenberg, Adam Logan and Akshay Venkatesh.
Keywords : Ceresa cycle; Ceresa class; nontriviality in the Griffiths group
11G30 - Curves of arbitrary genus or genus $\ne 1$ over global fields [See also 14H25]
11G40 - $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
14C25 - Algebraic cycles
14H25 - Arithmetic ground fields, See also {11Dxx,11G05,14Gxx}
14Q05 - Computational aspects of algebraic curves
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 28/06/2023 Conference Date : 06/06/2023 Subseries : Research talks arXiv category : Algebraic Geometry ; Number Theory Mathematical Area(s) : Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:00:07 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-06_srinivasan.mp4 
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Information on the Event
Event Title : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codesEvent Organizers : Anni, Samuele ; Bruin, Nils ; Kohel, David ; Martindale, Chloe Dates : 05/06/2023 - 09/06/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2889.html
Citation Data
DOI : 10.24350/CIRM.V.20054803Cite this video as: Srinivasan, Padmavathi (2023). Computing Ceresa classes of curves. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20054803 URI : http://dx.doi.org/10.24350/CIRM.V.20054803 |
See Also
- [Multi angle] An efficient break of the supersingular isogeny Diffie-Hellman protocol / Author of the conference Castryck, Wouter.
- [Multi angle] Probabilistic approaches to rational points on algebraic surfaces / Author of the conference Várilly-Alvarado, Anthony.
- [Multi angle] Isogeny-based cryptography on the (abelian) surface / Author of the conference Ti, Yan Bo.
- [Multi angle] The geometry of stable lattices in Bruhat-Tits buildings / Author of the conference Stanojkovski, Mima.
- [Multi angle] Counting S4 and S5 extensions satisfying the Hasse norm principle / Author of the conference Newton, Rachel.
Bibliography
- ELLENBERG, Jordan, LOGAN, Adam, SRINIVASAN, Padmavathi et VENKATESH, Akshay. Certifying nontriviality of Ceresa class of curve. In preparation. -
- BESSER, Amnon, SRINIVASAN, Padmavathi. Certifying nontriviality of the Ceresa cycle using p-adic integration. In préparation. -
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