LEADER 02675nam 2200517 450 001 996466562803316 005 20230421110211.0 010 $a3-030-57559-4 024 7 $a10.1007/978-3-030-57559-5 035 $a(CKB)4100000011794887 035 $a(DE-He213)978-3-030-57559-5 035 $a(MiAaPQ)EBC6513505 035 $a(Au-PeEL)EBL6513505 035 $a(OCoLC)1241732369 035 $a(PPN)254718930 035 $a(EXLCZ)994100000011794887 100 $a20211009d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aArakelov geometry and diophantine applications /$fEmmanuel Peyre, Gae?l Re?mond, editors 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (X, 469 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2276 311 $a3-030-57558-6 330 $aBridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2276 606 $aArakelov theory 606 $aGeometria algebraica$2thub 608 $aLlibres electrònics$2thub 615 0$aArakelov theory. 615 7$aGeometria algebraica 676 $a516.35 702 $aPeyre$b Emmanuel 702 $aRe?mond$b Gae?l 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466562803316 996 $aArakelov Geometry and Diophantine Applications$91768633 997 $aUNISA