2026-09-20T09:58:51Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/677852022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Kiran S. Kedlaya.
Balakrishnan, Jennifer Sayaka (Jennifer Shyamala Sayaka)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2011-12-19T18:51:14Z
2011-12-19T18:51:14Z
2011
2011
http://hdl.handle.net/1721.1/67785
767738207
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 171-175).
The Colemani integral is a p-adice line integral that can be used to encapsulate several quantities relevant, to a study of the arithmetic of varieties. In this thesis, I describe algorithms for computing Coleman integrals on hyperelliptic curves and discuss some immediate applications. I give algorithms to compute single and iterated integrals on odd models of hyperelliptic curves, as well as the necessary modifications to iplemieit these algorithms for even models. Furthermore, I show how these algorithinis can be used in various situations. The first application is the method of Chabatv to find rational points on curves of genus greater than 1. The second is Mlihyong Kim's recent nonabelian analogue of the Chabauty method for elliptic curves. The last two applications concern p-adic heights on Jacobians of hyperelliptic curves. necessary to formulate a p-adic analogue of the Birch and Swinnerton-Dyer conjecture. I conclude by stating the analogue of the Mazur-Tate-Teitelbaum conjecture iii our setting and presenting supporting data.
by Jennifer Sayaka Balakrishnan.
Ph.D.
175 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Coleman integration for hyperelliptic curves : algorithms and applications
Thesis
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Publication
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<Abstract>The Colemani integral is a p-adice line integral that can be used to encapsulate several quantities relevant, to a study of the arithmetic of varieties. In this thesis, I describe algorithms for computing Coleman integrals on hyperelliptic curves and discuss some immediate applications. I give algorithms to compute single and iterated integrals on odd models of hyperelliptic curves, as well as the necessary modifications to iplemieit these algorithms for even models. Furthermore, I show how these algorithinis can be used in various situations. The first application is the method of Chabatv to find rational points on curves of genus greater than 1. The second is Mlihyong Kim's recent nonabelian analogue of the Chabauty method for elliptic curves. The last two applications concern p-adic heights on Jacobians of hyperelliptic curves. necessary to formulate a p-adic analogue of the Birch and Swinnerton-Dyer conjecture. I conclude by stating the analogue of the Mazur-Tate-Teitelbaum conjecture iii our setting and presenting supporting data.</Abstract>
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