An analogue of Kida’s formula for elliptic curves with additive reduction
We study the Iwasawa theory of p -primary Selmer groups of elliptic curves E over a number field K . Assume that E has additive reduction at the primes of K above p . In this context, we prove that the Iwasawa invariants satisfy an analogue of the Riemann–Hurwitz formula. This generalizes a result o...
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| Veröffentlicht in: | The Ramanujan journal 2024-10, Vol.65 (2), p.857-883 |
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| container_title | The Ramanujan journal |
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| creator | Ray, Anwesh Shingavekar, Pratiksha |
| description | We study the Iwasawa theory of
p
-primary Selmer groups of elliptic curves
E
over a number field
K
. Assume that
E
has additive reduction at the primes of
K
above
p
. In this context, we prove that the Iwasawa invariants satisfy an analogue of the Riemann–Hurwitz formula. This generalizes a result of Hachimori and Matsuno. We apply our results to study rank stability questions for elliptic curves in prime cyclic extensions of
Q
. These extensions are ordered by their absolute discriminant and we prove an asymptotic lower bound for the density of extensions in which the Iwasawa invariants as well as the rank of the elliptic curve is stable. |
| doi_str_mv | 10.1007/s11139-024-00920-8 |
| format | Article |
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p
-primary Selmer groups of elliptic curves
E
over a number field
K
. Assume that
E
has additive reduction at the primes of
K
above
p
. In this context, we prove that the Iwasawa invariants satisfy an analogue of the Riemann–Hurwitz formula. This generalizes a result of Hachimori and Matsuno. We apply our results to study rank stability questions for elliptic curves in prime cyclic extensions of
Q
. These extensions are ordered by their absolute discriminant and we prove an asymptotic lower bound for the density of extensions in which the Iwasawa invariants as well as the rank of the elliptic curve is stable.</description><identifier>ISSN: 1382-4090</identifier><identifier>EISSN: 1572-9303</identifier><identifier>DOI: 10.1007/s11139-024-00920-8</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Curves ; Field theory ; Field Theory and Polynomials ; Fourier Analysis ; Functions of a Complex Variable ; Invariants ; Lower bounds ; Mathematics ; Mathematics and Statistics ; Number Theory</subject><ispartof>The Ramanujan journal, 2024-10, Vol.65 (2), p.857-883</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-fece4b4c7472da0d364e2a8488c37269f7fc551f33d64ae09db44c5ec39685aa3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11139-024-00920-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11139-024-00920-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Ray, Anwesh</creatorcontrib><creatorcontrib>Shingavekar, Pratiksha</creatorcontrib><title>An analogue of Kida’s formula for elliptic curves with additive reduction</title><title>The Ramanujan journal</title><addtitle>Ramanujan J</addtitle><description>We study the Iwasawa theory of
p
-primary Selmer groups of elliptic curves
E
over a number field
K
. Assume that
E
has additive reduction at the primes of
K
above
p
. In this context, we prove that the Iwasawa invariants satisfy an analogue of the Riemann–Hurwitz formula. This generalizes a result of Hachimori and Matsuno. We apply our results to study rank stability questions for elliptic curves in prime cyclic extensions of
Q
. These extensions are ordered by their absolute discriminant and we prove an asymptotic lower bound for the density of extensions in which the Iwasawa invariants as well as the rank of the elliptic curve is stable.</description><subject>Combinatorics</subject><subject>Curves</subject><subject>Field theory</subject><subject>Field Theory and Polynomials</subject><subject>Fourier Analysis</subject><subject>Functions of a Complex Variable</subject><subject>Invariants</subject><subject>Lower bounds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><issn>1382-4090</issn><issn>1572-9303</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kEtOwzAURS0EEqWwAUaWGBueP4njYVXxE5WYwNhy_Smu0qTYSREztsH2WAkpQWLG6L7BPVd6B6FzCpcUQF5lSilXBJggAIoBqQ7QhBaSEcWBHw43rxgRoOAYneS8BgABXE7Qw6zBpjF1u-o9bgN-iM58fXxmHNq06WuzT-zrOm67aLHt085n_Ba7F2yci13ceZy8620X2-YUHQVTZ3_2m1P0fHP9NL8ji8fb-_lsQSwD6Ejw1oulsFJI5gw4XgrPTCWqynLJShVksEVBA-euFMaDckshbOEtV2VVGMOn6GLc3ab2tfe50-u2T8MTWXMKinNZcDm02Niyqc05-aC3KW5MetcU9F6aHqXpQZr-kaarAeIjlIdys_Lpb_of6huDPHAp</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Ray, Anwesh</creator><creator>Shingavekar, Pratiksha</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20241001</creationdate><title>An analogue of Kida’s formula for elliptic curves with additive reduction</title><author>Ray, Anwesh ; Shingavekar, Pratiksha</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-fece4b4c7472da0d364e2a8488c37269f7fc551f33d64ae09db44c5ec39685aa3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Combinatorics</topic><topic>Curves</topic><topic>Field theory</topic><topic>Field Theory and Polynomials</topic><topic>Fourier Analysis</topic><topic>Functions of a Complex Variable</topic><topic>Invariants</topic><topic>Lower bounds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ray, Anwesh</creatorcontrib><creatorcontrib>Shingavekar, Pratiksha</creatorcontrib><collection>CrossRef</collection><jtitle>The Ramanujan journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ray, Anwesh</au><au>Shingavekar, Pratiksha</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An analogue of Kida’s formula for elliptic curves with additive reduction</atitle><jtitle>The Ramanujan journal</jtitle><stitle>Ramanujan J</stitle><date>2024-10-01</date><risdate>2024</risdate><volume>65</volume><issue>2</issue><spage>857</spage><epage>883</epage><pages>857-883</pages><issn>1382-4090</issn><eissn>1572-9303</eissn><abstract>We study the Iwasawa theory of
p
-primary Selmer groups of elliptic curves
E
over a number field
K
. Assume that
E
has additive reduction at the primes of
K
above
p
. In this context, we prove that the Iwasawa invariants satisfy an analogue of the Riemann–Hurwitz formula. This generalizes a result of Hachimori and Matsuno. We apply our results to study rank stability questions for elliptic curves in prime cyclic extensions of
Q
. These extensions are ordered by their absolute discriminant and we prove an asymptotic lower bound for the density of extensions in which the Iwasawa invariants as well as the rank of the elliptic curve is stable.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11139-024-00920-8</doi><tpages>27</tpages></addata></record> |
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| ispartof | The Ramanujan journal, 2024-10, Vol.65 (2), p.857-883 |
| issn | 1382-4090 1572-9303 |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Combinatorics Curves Field theory Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Invariants Lower bounds Mathematics Mathematics and Statistics Number Theory |
| title | An analogue of Kida’s formula for elliptic curves with additive reduction |
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