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Neron Models and Base Change
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133 b
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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 geometry.§
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