Divisibility results for zero-cycles
Let X be a product of smooth projective curves over a finite unramified extension k of Q p . Suppose that the Albanese variety of X has good reduction and that X has a k -rational point. We propose the following conjecture. The kernel of the Albanese map C H 0 ( X ) 0 → Alb X ( k ) is p -divisible....
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| Veröffentlicht in: | European journal of mathematics 2021-12, Vol.7 (4), p.1458-1501 |
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| container_title | European journal of mathematics |
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| creator | Gazaki, Evangelia Hiranouchi, Toshiro |
| description | Let
X
be a product of smooth projective curves over a finite unramified extension
k
of
Q
p
. Suppose that the Albanese variety of
X
has good reduction and that
X
has a
k
-rational point. We propose the following conjecture. The kernel of the Albanese map
C
H
0
(
X
)
0
→
Alb
X
(
k
)
is
p
-divisible. When
p
is an odd prime, we prove this conjecture for a large family of products of elliptic curves and certain principal homogeneous spaces of abelian varieties. Using this, we provide some evidence for a local-to-global conjecture for zero-cycles of Colliot-Thélène and Sansuc (Duke Math J 48(2):421–447, 1981), and Kato and Saito (Contemporary Mathematics, vol. 55:255–331, 1986). |
| doi_str_mv | 10.1007/s40879-021-00471-y |
| format | Article |
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X
be a product of smooth projective curves over a finite unramified extension
k
of
Q
p
. Suppose that the Albanese variety of
X
has good reduction and that
X
has a
k
-rational point. We propose the following conjecture. The kernel of the Albanese map
C
H
0
(
X
)
0
→
Alb
X
(
k
)
is
p
-divisible. When
p
is an odd prime, we prove this conjecture for a large family of products of elliptic curves and certain principal homogeneous spaces of abelian varieties. Using this, we provide some evidence for a local-to-global conjecture for zero-cycles of Colliot-Thélène and Sansuc (Duke Math J 48(2):421–447, 1981), and Kato and Saito (Contemporary Mathematics, vol. 55:255–331, 1986).</description><identifier>ISSN: 2199-675X</identifier><identifier>EISSN: 2199-6768</identifier><identifier>DOI: 10.1007/s40879-021-00471-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algebraic Geometry ; Curves ; Mathematics ; Mathematics and Statistics ; Research Article</subject><ispartof>European journal of mathematics, 2021-12, Vol.7 (4), p.1458-1501</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021.</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-8c76dd0c38617ac0f80661d60917271aeb9ec7f8f78cf1fc46e710374fae5e023</citedby><cites>FETCH-LOGICAL-c319t-8c76dd0c38617ac0f80661d60917271aeb9ec7f8f78cf1fc46e710374fae5e023</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/s40879-021-00471-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40879-021-00471-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Gazaki, Evangelia</creatorcontrib><creatorcontrib>Hiranouchi, Toshiro</creatorcontrib><title>Divisibility results for zero-cycles</title><title>European journal of mathematics</title><addtitle>European Journal of Mathematics</addtitle><description>Let
X
be a product of smooth projective curves over a finite unramified extension
k
of
Q
p
. Suppose that the Albanese variety of
X
has good reduction and that
X
has a
k
-rational point. We propose the following conjecture. The kernel of the Albanese map
C
H
0
(
X
)
0
→
Alb
X
(
k
)
is
p
-divisible. When
p
is an odd prime, we prove this conjecture for a large family of products of elliptic curves and certain principal homogeneous spaces of abelian varieties. Using this, we provide some evidence for a local-to-global conjecture for zero-cycles of Colliot-Thélène and Sansuc (Duke Math J 48(2):421–447, 1981), and Kato and Saito (Contemporary Mathematics, vol. 55:255–331, 1986).</description><subject>Algebraic Geometry</subject><subject>Curves</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Research Article</subject><issn>2199-675X</issn><issn>2199-6768</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouKz7BzwV9BqdSdpMcpT1Exa8KHgL3TSRSN2uSVeov95qRW-eZhie9x14GDtGOEMAOs8laDIcBHKAkpAPe2wm0BiuSOn93716OmSLnOMaJAolJZYzdnoZ3-N4im3shyL5vGv7XIQuFR8-ddwNrvX5iB2Eus1-8TPn7PH66mF5y1f3N3fLixV3Ek3PtSPVNOCkVki1g6BBKWwUGCRBWPu18Y6CDqRdwOBK5QlBUhlqX3kQcs5Opt5t6t52Pvf2pdulzfjSispoVVFlYKTERLnU5Zx8sNsUX-s0WAT7JcROQuwoxH4LscMYklMoj_Dm2ae_6n9Sn2l1Yto</recordid><startdate>20211201</startdate><enddate>20211201</enddate><creator>Gazaki, Evangelia</creator><creator>Hiranouchi, Toshiro</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20211201</creationdate><title>Divisibility results for zero-cycles</title><author>Gazaki, Evangelia ; Hiranouchi, Toshiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-8c76dd0c38617ac0f80661d60917271aeb9ec7f8f78cf1fc46e710374fae5e023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebraic Geometry</topic><topic>Curves</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Research Article</topic><toplevel>online_resources</toplevel><creatorcontrib>Gazaki, Evangelia</creatorcontrib><creatorcontrib>Hiranouchi, Toshiro</creatorcontrib><collection>CrossRef</collection><jtitle>European journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gazaki, Evangelia</au><au>Hiranouchi, Toshiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Divisibility results for zero-cycles</atitle><jtitle>European journal of mathematics</jtitle><stitle>European Journal of Mathematics</stitle><date>2021-12-01</date><risdate>2021</risdate><volume>7</volume><issue>4</issue><spage>1458</spage><epage>1501</epage><pages>1458-1501</pages><issn>2199-675X</issn><eissn>2199-6768</eissn><abstract>Let
X
be a product of smooth projective curves over a finite unramified extension
k
of
Q
p
. Suppose that the Albanese variety of
X
has good reduction and that
X
has a
k
-rational point. We propose the following conjecture. The kernel of the Albanese map
C
H
0
(
X
)
0
→
Alb
X
(
k
)
is
p
-divisible. When
p
is an odd prime, we prove this conjecture for a large family of products of elliptic curves and certain principal homogeneous spaces of abelian varieties. Using this, we provide some evidence for a local-to-global conjecture for zero-cycles of Colliot-Thélène and Sansuc (Duke Math J 48(2):421–447, 1981), and Kato and Saito (Contemporary Mathematics, vol. 55:255–331, 1986).</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40879-021-00471-y</doi><tpages>44</tpages></addata></record> |
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| identifier | ISSN: 2199-675X |
| ispartof | European journal of mathematics, 2021-12, Vol.7 (4), p.1458-1501 |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Curves Mathematics Mathematics and Statistics Research Article |
| title | Divisibility results for zero-cycles |
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