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035   $a(DE-B1597)9781400824885
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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   $a0-691-09150-1 
311   $a0-691-09151-X 
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
610   $aAbelian variety.
610   $aAbsolute continuity.
610   $aAddition.
610   $aAffine space.
610   $aAlgebraically closed field.
610   $aAmbient space.
610   $aAverage.
610   $aBetti number.
610   $aBirch and Swinnerton-Dyer conjecture.
610   $aBlowing up.
610   $aCodimension.
610   $aCoefficient.
610   $aComputation.
610   $aConjecture.
610   $aConjugacy class.
610   $aConvolution.
610   $aCritical value.
610   $aDifferential geometry of surfaces.
610   $aDimension (vector space).
610   $aDimension.
610   $aDirect sum.
610   $aDivisor (algebraic geometry).
610   $aDivisor.
610   $aEigenvalues and eigenvectors.
610   $aElliptic curve.
610   $aEquation.
610   $aEquidistribution theorem.
610   $aExistential quantification.
610   $aFactorization.
610   $aFinite field.
610   $aFinite group.
610   $aFinite set.
610   $aFlat map.
610   $aFourier transform.
610   $aFunction field.
610   $aFunctional equation.
610   $aGoursat's lemma.
610   $aGround field.
610   $aGroup representation.
610   $aHyperplane.
610   $aHypersurface.
610   $aInteger matrix.
610   $aInteger.
610   $aIrreducible component.
610   $aIrreducible polynomial.
610   $aIrreducible representation.
610   $aJ-invariant.
610   $aK3 surface.
610   $aL-function.
610   $aLebesgue measure.
610   $aLefschetz pencil.
610   $aLevel of measurement.
610   $aLie algebra.
610   $aLimit superior and limit inferior.
610   $aMinimal polynomial (field theory).
610   $aModular form.
610   $aMonodromy.
610   $aMorphism.
610   $aNumerical analysis.
610   $aOrthogonal group.
610   $aPercentage.
610   $aPolynomial.
610   $aPrime number.
610   $aProbability measure.
610   $aQuadratic function.
610   $aQuantity.
610   $aQuotient space (topology).
610   $aRepresentation theory.
610   $aResidue field.
610   $aRiemann hypothesis.
610   $aRoot of unity.
610   $aScalar (physics).
610   $aSet (mathematics).
610   $aSheaf (mathematics).
610   $aSubgroup.
610   $aSummation.
610   $aSymmetric group.
610   $aSystem of imprimitivity.
610   $aTheorem.
610   $aTrivial representation.
610   $aZariski topology.
615  0$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   $a9910821229203321
996   $aTwisted L-Functions and Monodromy$9377608
997   $aUNINA