LEADER 03606nam 2200589 450 001 996466621003316 005 20220303125330.0 010 $a3-540-46209-0 024 7 $a10.1007/BFb0084525 035 $a(CKB)1000000000437428 035 $a(SSID)ssj0000321737 035 $a(PQKBManifestationID)12041906 035 $a(PQKBTitleCode)TC0000321737 035 $a(PQKBWorkID)10279774 035 $a(PQKB)10605162 035 $a(DE-He213)978-3-540-46209-5 035 $a(MiAaPQ)EBC5595676 035 $a(Au-PeEL)EBL5595676 035 $a(OCoLC)1076244168 035 $a(MiAaPQ)EBC6842794 035 $a(Au-PeEL)EBL6842794 035 $a(OCoLC)793079161 035 $a(PPN)155193686 035 $a(EXLCZ)991000000000437428 100 $a20220303d1989 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aCapacity theory on algebraic curves /$fRobert S. Rumely 205 $a1st ed. 1989. 210 1$aBerlin :$cSpringer-Verlag,$d[1989] 210 4$d©1989 215 $a1 online resource (VI, 438 p.) 225 1 $aLecture notes in mathematics ;$v1378 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-51410-4 327 $aPreliminaries -- Foundations -- The canonical distance -- Local capacity theory ? Archimedean case -- Local capacity theory ? Nonarchimedean case -- Global capacity theory -- Applications. 330 $aCapacity is a measure of size for sets, with diverse applications in potential theory, probability and number theory. This book lays foundations for a theory of capacity for adelic sets on algebraic curves. Its main result is an arithmetic one, a generalization of a theorem of Fekete and Szegö which gives a sharp existence/finiteness criterion for algebraic points whose conjugates lie near a specified set on a curve. The book brings out a deep connection between the classical Green's functions of analysis and Néron's local height pairings; it also points to an interpretation of capacity as a kind of intersection index in the framework of Arakelov Theory. It is a research monograph and will primarily be of interest to number theorists and algebraic geometers; because of applications of the theory, it may also be of interest to logicians. The theory presented generalizes one due to David Cantor for the projective line. As with most adelic theories, it has a local and a global part. Let /K be a smooth, complete curve over a global field; let Kv denote the algebraic closure of any completion of K. The book first develops capacity theory over local fields, defining analogues of the classical logarithmic capacity and Green's functions for sets in (Kv). It then develops a global theory, defining the capacity of a galois-stable set in (Kv) relative to an effictive global algebraic divisor. The main technical result is the construction of global algebraic functions whose logarithms closely approximate Green's functions at all places of K. These functions are used in proving the generalized Fekete-Szegö theorem; because of their mapping properties, they may be expected to have other applications as well. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1378. 606 $aGeometry, Algebraic 615 0$aGeometry, Algebraic. 676 $a516.35 700 $aRumely$b Robert$f1952-$058689 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466621003316 996 $aCapacity theory on algebraic curves$978588 997 $aUNISA