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020 _a9783319266381
_9978-3-319-26638-1
024 7 _a10.1007/978-3-319-26638-1
_2doi
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072 7 _aMAT012010
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072 7 _aPBMW
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082 0 4 _a516.35
_223
100 1 _aHalle, Lars Halvard.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aNéron Models and Base Change
_h[electronic resource] /
_cby Lars Halvard Halle, Johannes Nicaise.
250 _a1st ed. 2016.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aX, 151 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
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347 _atext file
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490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2156
505 0 _aNormal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Introduction -- Preliminaries -- Models of curves and the Neron component series of a Jacobian -- Component groups and non-archimedean uniformization -- The base change conductor and Edixhoven's ltration -- The base change conductor and the Artin conductor -- Motivic zeta functions of semi-abelian varieties -- Cohomological interpretation of the motivic zeta function. /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0in; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}.
520 _aPresenting the first systematic treatment of the behavior of Néron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to Néron models of semi-abelian varieties, motivated by concrete research problems and complemented with explicit examples. Néron models of abelian and semi-abelian varieties have become an indispensable tool in algebraic and arithmetic geometry since Néron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodge theory. We focus specifically on Néron component groups, Edixhoven’s filtration and the base change conductor of Chai and Yu, and we study these invariants using various techniques such as models of curves, sheaves on Grothendieck sites and non-archimedean uniformization. We then apply our results to the study of motivic zeta functions of abelian varieties. The final chapter contains a list of challenging open questions. This book is aimed towards researchers with a background in algebraic and arithmetic geometry.
650 0 _aAlgebraic geometry.
650 0 _aNumber theory.
650 1 4 _aAlgebraic Geometry.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11019
650 2 4 _aNumber Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M25001
700 1 _aNicaise, Johannes.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319266374
776 0 8 _iPrinted edition:
_z9783319266398
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2156
856 4 0 _uhttps://doi.org/10.1007/978-3-319-26638-1
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