LEADER 07005nam 22017175 450 001 9910154746203321 005 20230808192331.0 010 $a1-4008-8259-1 024 7 $a10.1515/9781400882595 035 $a(CKB)3710000000628084 035 $a(MiAaPQ)EBC4738753 035 $a(DE-B1597)467916 035 $a(OCoLC)979743328 035 $a(DE-B1597)9781400882595 035 $a(EXLCZ)993710000000628084 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aRigid Local Systems. (AM-139), Volume 139 /$fNicholas M. Katz 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$dİ1996 215 $a1 online resource (233 pages) 225 0 $aAnnals of Mathematics Studies ;$v321 311 $a0-691-01119-2 311 $a0-691-01118-4 320 $aIncludes bibliographical references. 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tCHAPTER 1. First results on rigid local systems -- $tCHAPTER 2. The theory of middle convolution -- $tCHAPTER 3. Fourier Transform and rigidity -- $tCHAPTER 4. Middle convolution: dependence on parameters -- $tCHAPTER 5. Structure of rigid local systems -- $tCHAPTER 6. Existence algorithms for rigids -- $tCHAPTER 7. Diophantine aspects of rigidity -- $tCHAPTER 8. Motivic description of rigids -- $tCHAPTER 9. Grothendieck's p-curvature conjecture for rigids -- $tReferences 330 $aRiemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1,infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard nth order generalizations of the hypergeometric function, n F n-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the l-adic Fourier Transform. 410 0$aAnnals of mathematics studies ;$vno. 139. 606 $aDifferential equations$xNumerical solutions 606 $aHypergeometric functions 606 $aSheaf theory 610 $aAdditive group. 610 $aAlexander Grothendieck. 610 $aAlgebraic closure. 610 $aAlgebraic differential equation. 610 $aAlgebraically closed field. 610 $aAlgorithm. 610 $aAnalytic continuation. 610 $aAutomorphism. 610 $aAxiom of choice. 610 $aBernhard Riemann. 610 $aBig O notation. 610 $aCalculation. 610 $aCarlos Simpson. 610 $aCoefficient. 610 $aCohomology. 610 $aCommutator. 610 $aCompactification (mathematics). 610 $aComparison theorem. 610 $aComplex analytic space. 610 $aComplex conjugate. 610 $aComplex manifold. 610 $aConjecture. 610 $aConjugacy class. 610 $aConvolution. 610 $aCorollary. 610 $aCube root. 610 $aCusp form. 610 $aDe Rham cohomology. 610 $aDifferential equation. 610 $aDimension. 610 $aDimensional analysis. 610 $aDiscrete valuation ring. 610 $aDisjoint union. 610 $aDivisor. 610 $aDuality (mathematics). 610 $aEigenfunction. 610 $aEigenvalues and eigenvectors. 610 $aElliptic curve. 610 $aEquation. 610 $aEquivalence of categories. 610 $aExact sequence. 610 $aExistential quantification. 610 $aFinite field. 610 $aFinite set. 610 $aFourier transform. 610 $aFunctor. 610 $aFundamental group. 610 $aGeneric point. 610 $aGround field. 610 $aHodge structure. 610 $aHypergeometric function. 610 $aInteger. 610 $aInvertible matrix. 610 $aIsomorphism class. 610 $aJordan normal form. 610 $aLevel of measurement. 610 $aLinear differential equation. 610 $aLocal system. 610 $aMathematical induction. 610 $aMathematics. 610 $aMatrix (mathematics). 610 $aMonodromy. 610 $aMonomial. 610 $aMorphism. 610 $aNatural filtration. 610 $aParameter. 610 $aParity (mathematics). 610 $aPerfect field. 610 $aPerverse sheaf. 610 $aPolynomial. 610 $aPrime number. 610 $aProjective representation. 610 $aProjective space. 610 $aPullback (category theory). 610 $aPullback. 610 $aRational function. 610 $aRegular singular point. 610 $aRelative dimension. 610 $aResidue field. 610 $aRing of integers. 610 $aRoot of unity. 610 $aSequence. 610 $aSesquilinear form. 610 $aSet (mathematics). 610 $aSheaf (mathematics). 610 $aSix operations. 610 $aSpecial case. 610 $aSubgroup. 610 $aSubobject. 610 $aSubring. 610 $aSuggestion. 610 $aSummation. 610 $aTensor product. 610 $aTheorem. 610 $aTheory. 610 $aTopology. 610 $aTriangular matrix. 610 $aTrivial representation. 610 $aVector space. 610 $aZariski topology. 615 0$aDifferential equations$xNumerical solutions. 615 0$aHypergeometric functions. 615 0$aSheaf theory. 676 $a515/.35 700 $aKatz$b Nicholas M., $059374 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154746203321 996 $aRigid Local Systems. (AM-139), Volume 139$92839575 997 $aUNINA