UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC
We present a heuristic argument based on Honda–Tate theory against many conjectures in ‘unlikely intersections’ over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian. Using methods of additive combinatorics, we answe...
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| Format: | Article |
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Cambridge University Press (CUP)
2019
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| Online Access: | https://hdl.handle.net/1721.1/122793 |
| _version_ | 1826192389591531520 |
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| author | Shankar, Ananth Tsimerman, Jacob |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Shankar, Ananth Tsimerman, Jacob |
| author_sort | Shankar, Ananth |
| collection | MIT |
| description | We present a heuristic argument based on Honda–Tate theory against many conjectures in ‘unlikely intersections’ over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian. Using methods of additive combinatorics, we answer a related question of Chai and Oort where the ambient Shimura variety is a power of the modular curve. |
| first_indexed | 2024-09-23T09:10:57Z |
| format | Article |
| id | mit-1721.1/122793 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:10:57Z |
| publishDate | 2019 |
| publisher | Cambridge University Press (CUP) |
| record_format | dspace |
| spelling | mit-1721.1/1227932022-09-26T10:59:32Z UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC Shankar, Ananth Tsimerman, Jacob Massachusetts Institute of Technology. Department of Mathematics We present a heuristic argument based on Honda–Tate theory against many conjectures in ‘unlikely intersections’ over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian. Using methods of additive combinatorics, we answer a related question of Chai and Oort where the ambient Shimura variety is a power of the modular curve. 2019-11-07T18:06:42Z 2019-11-07T18:06:42Z 2018-08 Article http://purl.org/eprint/type/JournalArticle 2050-5094 https://hdl.handle.net/1721.1/122793 Shankar, A. and Tsimerman, J. UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC. Forum of Mathematics, Sigma, 6 (August 2018): E13 © 2018 The Author(s) 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 10.1017/fms.2018.15 http://dx.doi.org/10.1017/fms.2018.15 Forum of Mathematics, Sigma Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Cambridge University Press (CUP) Cambridge University Press |
| spellingShingle | Shankar, Ananth Tsimerman, Jacob UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC |
| title | UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC |
| title_full | UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC |
| title_fullStr | UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC |
| title_full_unstemmed | UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC |
| title_short | UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC |
| title_sort | unlikely intersections in finite characteristic |
| url | https://hdl.handle.net/1721.1/122793 |
| work_keys_str_mv | AT shankarananth unlikelyintersectionsinfinitecharacteristic AT tsimermanjacob unlikelyintersectionsinfinitecharacteristic |