MARC Record from marc_columbia

LEADER: 02683cam a22003374a 4500
001 5456340
005 20221110041312.0
008 050503t20052005riu b 001 0 eng
010 $a 2005048051
020 $a0821838628 (alk. paper)
035 $a(OCoLC)ocm60321615
035 $a(NNC)5456340
035 $a5456340
040 $aDLC$cDLC$dBAKER$dC#P$dOrLoB-B
042 $apcc
050 00 $aQA242.5$b.B85 2005
082 00 $a516.3/5$222
100 1 $aBuium, Alexandru,$d1955-$0http://id.loc.gov/authorities/names/n85280601
245 10 $aArithmetic differential equations /$cAlexandru Buium.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$c[2005], ©2005.
300 $axxxii, 310 pages ;$c27 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aMathematical surveys and monographs ;$vv. 118
504 $aIncludes bibliographical references (p. 301-305) and index.
505 00 $gPt. 1.$tMain concepts and results -- $gCh. 1.$tPreliminaries from algebraic geometry -- $gCh. 2.$tOutline of [delta] - geometry -- $gPt. 2.$tGeneral theory -- $gCh. 3.$tGlobal theory -- $gCh. 4.$tLocal theory -- $gCh. 5.$tBirational theory -- $gPt. 3.$tApplications -- $gCh. 6.$tSpherical correspondences -- $gCh. 7.$tFlat correspondences -- $gCh. 8.$tHyperbolic correspondences.
520 1 $a"This research monograph develops an arithmetic analogue of the theory of ordinary differential equations: functions are replaced here by integer numbers, the derivative operator is replaced by a "Fermat quotient operator", and differential equations (viewed as functions on jet spaces) are replaced by "arithmetic differential equations". The main application of this theory concerns the construction and study of quotients of algebraic curves by correspondences with infinite orbits. Any such quotient reduces to a point in usual algebraic geometry. But many quotients as above cease to be trivial (and become quite interesting) if one enlarges algebraic geometry by using arithmetic differential equations in place of algebraic equations. The book partly follows a series of papers written by the author; however, a substantial part of the material presented here has never been published before. For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.
650 0 $aArithmetical algebraic geometry.$0http://id.loc.gov/authorities/subjects/sh87002041
650 0 $aRiemann surfaces.$0http://id.loc.gov/authorities/subjects/sh85114044
830 0 $aMathematical surveys and monographs ;$vno. 118.$0http://id.loc.gov/authorities/names/n83732928
852 00 $bmat$hQA242.5$i.B85 2005