LEADER 03677nam 2200745 a 450 001 9910969267003321 005 20251117064840.0 010 $a9786612820892 010 $a9781282820890 010 $a1282820893 010 $a9781400824885 010 $a1400824885 024 7 $a10.1515/9781400824885 035 $a(CKB)2670000000069015 035 $a(EBL)617335 035 $a(OCoLC)670429607 035 $a(SSID)ssj0000409573 035 $a(PQKBManifestationID)11314021 035 $a(PQKBTitleCode)TC0000409573 035 $a(PQKBWorkID)10348703 035 $a(PQKB)11056699 035 $a(DE-B1597)446168 035 $a(OCoLC)979910656 035 $a(DE-B1597)9781400824885 035 $a(Au-PeEL)EBL617335 035 $a(CaPaEBR)ebr10421690 035 $a(CaONFJC)MIL282089 035 $a(MiAaPQ)EBC617335 035 $a(Perlego)734146 035 $a(iGPub)PUPB0001665 035 $a(EXLCZ)992670000000069015 100 $a20010501d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTwisted L-functions and monodromy /$fby Nicholas M. Katz 205 $aCore Textbook 210 $aPrinceton $cPrinceton University Press$d2002 215 $a1 online resource (258 p.) 225 1 $aAnnals of mathematics studies ;$vno. 150 300 $aDescription based upon print version of record. 311 08$a9780691091501 311 08$a0691091501 311 08$a9780691091518 311 08$a069109151X 320 $aIncludes bibliographical references (p. [235]-239) and index. 327 $apt. 1. Background material -- pt. 2. Twist sheaves, over an algebraically closed field -- pt. 3. Twist sheaves, over a finite field -- pt. 4. Twist sheaves over schemes of finite type over Z. 330 $aFor hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry. 410 0$aAnnals of mathematics studies ;$vno. 150. 606 $aL-functions 606 $aMonodromy groups 615 0$aL-functions. 615 0$aMonodromy groups. 676 $a512/.74 686 $aSI 830$2rvk 700 $aKatz$b Nicholas M.$f1943-$059374 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910969267003321 996 $aTwisted L-Functions and Monodromy$9377608 997 $aUNINA