03854nam a2200433 i 4500991003554909707536m o d cr cn ---mpcbr181008s2016 sz | o j |||| 0|eng d978331926638110.1007/978-3-319-26638-1doib14351389-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng516.3523AMS 14K15AMS 14G10AMS 14G22LC QA564-609Halle, Lars Halvard721076Néron Models and Base Change[e-book] /by Lars Halvard Halle, Johannes NicaiseCham :Springer International Publishing,20161 online resource (x, 151 p.)texttxtrdacontentunmediatednrdamediavolumencrdacarrierLecture Notes in Mathematics,0075-8434 ;2156Normal 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;}Presenting 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 geometryGeometry, AlgebraicNumber theoryNicaise, Johannesauthorhttp://id.loc.gov/vocabulary/relators/aut721075Springer eBooksPrinted edition:9783319266374https://link.springer.com/book/10.1007/978-3-319-26638-1#aboutAn electronic book accessible through the World Wide Web.b1435138903-03-2208-10-18991003554909707536Néron models and base change1412588UNISALENTOle01308-10-18m@ -engsz 00