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035   $a(DE-B1597)9781400882120
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100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aGauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116 /$fNicholas M. Katz
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©1988
215   $a1 online resource (257 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v338
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08432-7 
311   $a0-691-08433-5 
320   $aBibliography.
327   $tFrontmatter -- $tContents -- $tIntroduction -- $tCHAPTER 1. Breaks and Swan Conductors -- $tCHAPTER 2. Curves and Their Cohomology -- $tCHAPTER 3. Equidistribution in Equal Characteristic -- $tCHAPTER 4. Gauss Sums and Kloosterman Sums: Kloosterman Sheaves -- $tCHAPTER 5. Convolution of Sheaves on Gm -- $tCHAPTER 6. Local Convolution -- $tCHAPTER 7. Local Monodromy at Zero of a Convolution: Detailed Study -- $tCHAPTER 8. Complements on Convolution -- $tCHAPTER 9. Equidistribution in (S1)r of r-tuples of Angles of Gauss Sums -- $tCHAPTER 10. Local Monodromy at ? of Kloosterman Sheaves -- $tCHAPTER 11. Global Monodromy of Kloosterman Sheaves -- $tCHAPTER 12. Integral Monodromy of Kloosterman Sheaves (d'après O. Gabber) -- $tCHAPTER 13. Equidistribution of "Angles" of Kloosterman Sums -- $tReferences
330   $aThe study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.
410  0$aAnnals of mathematics studies ;$vno. 116.
606   $aGaussian sums
606   $aKloosterman sums
606   $aHomology theory
606   $aMonodromy groups
610   $aAbelian category.
610   $aAbsolute Galois group.
610   $aAbsolute value.
610   $aAdditive group.
610   $aAdjoint representation.
610   $aAffine variety.
610   $aAlgebraic group.
610   $aAutomorphic form.
610   $aAutomorphism.
610   $aBig O notation.
610   $aCartan subalgebra.
610   $aCharacteristic polynomial.
610   $aClassification theorem.
610   $aCoefficient.
610   $aCohomology.
610   $aCokernel.
610   $aCombination.
610   $aCommutator.
610   $aCompactification (mathematics).
610   $aComplex Lie group.
610   $aComplex number.
610   $aConjugacy class.
610   $aContinuous function.
610   $aConvolution theorem.
610   $aConvolution.
610   $aDeterminant.
610   $aDiagonal matrix.
610   $aDimension (vector space).
610   $aDirect sum.
610   $aDual basis.
610   $aEigenvalues and eigenvectors.
610   $aEmpty set.
610   $aEndomorphism.
610   $aEquidistribution theorem.
610   $aEstimation.
610   $aExactness.
610   $aExistential quantification.
610   $aExponential sum.
610   $aExterior algebra.
610   $aFaithful representation.
610   $aFinite field.
610   $aFinite group.
610   $aFour-dimensional space.
610   $aFrobenius endomorphism.
610   $aFundamental group.
610   $aFundamental representation.
610   $aGalois group.
610   $aGauss sum.
610   $aHomomorphism.
610   $aInteger.
610   $aIrreducibility (mathematics).
610   $aIsomorphism class.
610   $aKloosterman sum.
610   $aL-function.
610   $aLeray spectral sequence.
610   $aLie algebra.
610   $aLie theory.
610   $aMaximal compact subgroup.
610   $aMethod of moments (statistics).
610   $aMonodromy theorem.
610   $aMonodromy.
610   $aMorphism.
610   $aMultiplicative group.
610   $aNatural number.
610   $aNilpotent.
610   $aOpen problem.
610   $aP-group.
610   $aPairing.
610   $aParameter space.
610   $aParameter.
610   $aPartially ordered set.
610   $aPerfect field.
610   $aPoint at infinity.
610   $aPolynomial ring.
610   $aPrime number.
610   $aQuotient group.
610   $aRepresentation ring.
610   $aRepresentation theory.
610   $aResidue field.
610   $aRiemann hypothesis.
610   $aRoot of unity.
610   $aSheaf (mathematics).
610   $aSimple Lie group.
610   $aSkew-symmetric matrix.
610   $aSmooth morphism.
610   $aSpecial case.
610   $aSpin representation.
610   $aSubgroup.
610   $aSupport (mathematics).
610   $aSymmetric matrix.
610   $aSymplectic group.
610   $aSymplectic vector space.
610   $aTensor product.
610   $aTheorem.
610   $aTrace (linear algebra).
610   $aTrivial representation.
610   $aVariable (mathematics).
610   $aWeil conjectures.
610   $aWeyl character formula.
610   $aZariski topology.
615  0$aGaussian sums.
615  0$aKloosterman sums.
615  0$aHomology theory.
615  0$aMonodromy groups.
676   $a512/.7
700   $aKatz$b Nicholas M., $059374
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154750003321
996   $aGauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116$92788797
997   $aUNINA