LEADER 05974nam 22008535 450 001 9910299994203321 005 20200701145049.0 010 $a3-642-55245-5 024 7 $a10.1007/978-3-642-55245-8 035 $a(CKB)3710000000315887 035 $a(EBL)1968573 035 $a(OCoLC)898028341 035 $a(SSID)ssj0001408284 035 $a(PQKBManifestationID)11797477 035 $a(PQKBTitleCode)TC0001408284 035 $a(PQKBWorkID)11346332 035 $a(PQKB)10652629 035 $a(MiAaPQ)EBC1968573 035 $a(DE-He213)978-3-642-55245-8 035 $a(PPN)183150244 035 $a(EXLCZ)993710000000315887 100 $a20141208d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIwasawa Theory 2012 $eState of the Art and Recent Advances /$fedited by Thanasis Bouganis, Otmar Venjakob 205 $a1st ed. 2014. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014. 215 $a1 online resource (486 p.) 225 1 $aContributions in Mathematical and Computational Sciences,$x2191-303X ;$v7 300 $a"The great interest in Iwasawa Theory is reflected by the highly successful bi-annual series of international conferences, starting in 2004 in Besancon and continuing in Limoges, Irsee and Toronto with a scientific committee formed by John Coates, Ralph Greenberg, Cornelius Greither, Masato Kurihara, and Thong Nguyen Quang Do"--Preface. 311 $a3-642-55244-7 320 $aIncludes bibliographical references at the end of each chapters. 327 $aLecture notes: C. Wuthrich: Overview of some Iwasawa theory -- X. Wan: Introduction to Skinner-Urban's work on the Iwasawa main conjecture for GL -- Research and Survey articles: D. Benois: On extra zeros of p-adic L-functions: the crystalline case -- Th. Bouganis: On special L-values attached to Siegel modular forms -- T. Fukaya et al: Modular symbols in Iwasawa theory -- T. Fukuda et al: Weber's class number one problem -- R. Greenberg: On p-adic Artin L-functions II -- M.-L. Hsieh: Iwasawa ?-invariants of p-adic Hecke L-functions -- S. Kobayashi: The p-adic height pairing on abelian varieties at non-ordinary primes -- J. Kohlhaase: Iwasawa modules arising from deformation spaces of p-divisible formal group laws -- M. Kurihara: The structure of Selmer groups for elliptic curves and modular symbols -- D. Loeffler: P-adic integration on ray class groups and non-ordinary p-adic L-functions -- T. Nguyen Quang Do: On equivariant characteristic ideals of real classes -- E. Urban: Nearly over convergent modular forms -- M. Witte: Non-commutative L-functions for varieties over finite fields -- Z. Wojtkowiak: On $\widehat{\mathbb{Z}}$-zeta function. 330 $aThis is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida?s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan). 410 0$aContributions in Mathematical and Computational Sciences,$x2191-303X ;$v7 606 $aNumber theory 606 $aAlgebraic geometry 606 $aK-theory 606 $aTopological groups 606 $aLie groups 606 $aAlgebra 606 $aFunctions of complex variables 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 615 0$aNumber theory. 615 0$aAlgebraic geometry. 615 0$aK-theory. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aAlgebra. 615 0$aFunctions of complex variables. 615 14$aNumber Theory. 615 24$aAlgebraic Geometry. 615 24$aK-Theory. 615 24$aTopological Groups, Lie Groups. 615 24$aAlgebra. 615 24$aFunctions of a Complex Variable. 676 $a512.3 702 $aBouganis$b Thanasis$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aVenjakob$b Otmar$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299994203321 996 $aIwasawa theory 2012$91409985 997 $aUNINA