دانلود کتاب Moments, Monodromy, and Perversity. (AM-159): A Diophantine Perspective. (AM-159)

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Contents\nIntroduction\nChapter 1: Basic results on perversity and higher moments\n (1.1) The notion of a d-separating space of functions\n (1.2) Review of semiperversity and perversity\n (1.3) A twisting construction: the object Twist(L,K,F,h)\n (1.4) The basic theorem and its consequences\n (1.5) Review of weights\n (1.6) Remarks on the various notions of mixedness\n (1.7) The Orthogonality Theorem\n (1.8) First Applications of the Orthogonality Theorem\n (1.9) Questions of autoduality: the Frobenius-Schur indicator theorem\n (1.10) Dividing out the \"constant part\" of an ɩ-pure perverse sheaf\n (1.11) The subsheaf Nncst0 in the mixed case\n (1.12) Interlude: abstract trace functions; approximate trace functions\n (1.13) Two uniqueness theorems\n (1.14) The central normalization F0 of a trace function F\n (1.15) First applications to the objects Twist(L,K,F,h): The notion of standard input\n (1.16) Review of higher moments\n (1.17) Higher moments for geometrically irreducible lisse sheaves\n (1.18) Higher moments for geometrically irreducible perverse sheaves\n (1.19) A fundamental inequality\n (1.20) Higher moment estimates for Twist(L,K,F,h)\n (1.21) Proof of the Higher Moment Theorem 1.20.2: combinatorial preliminaries\n (1.22) Variations on the Higher Moment Theorem\n (1.23) Counterexamples\nChapter 2: How to apply the results of Chapter 1\n (2.1) How to apply the Higher Moment Theorem\n (2.2) Larsen\'s Alternative\n (2.3) Larsen\'s Eighth Moment Conjecture\n (2.4) Remarks on Larsen\'s Eighth Moment Conjecture\n (2.5) How to apply Larsen\'s Eighth Moment Conjecture; its current status\n (2.6) Other tools to rule out finiteness of Ggeom\n (2.7) Some conjectures on drops\n (2.8) More tools to rule out finiteness of Ggeom: sheaves of perverse origin and their monodromy\nChapter 3: Additive character sums on An\n (3.1) The theorem\n (3.2) Proof of the LΨ Theorem 3.1.2\n (3.3) Interlude: the homothety contraction method\n (3.4) Return to the proof of the LΨ theorem\n (3.5) Monodromy of exponential sums of Deligne type on An\n (3.6) Interlude: an exponential sum calculation\n (3.7) Interlude: separation of variables\n (3.8) Return to the monodromy of exponential sums of Deligne type on A^n\n (3.9) Application to Deligne polynomials\n (3.10) Self dual families of Deligne polynomials\n (3.11) Proofs of the theorems on self dual families\n (3.12) Proof of Theorem 3.10.7\n (3.13) Proof of Theorem 3.10.9\nChapter 4: Additive character sums on more general X\n (4.1) The general setting\n (4.2) The perverse sheaf M(X, r, Zi\'s, ei‘s, Ψ) on P(e1, ..., er)\n (4.3) Interlude An exponential sum identity\n (4.4) Return to the proof of Theorem 4.2.12\n (4.5) The subcases n = 1 and n = 2\nChapter 5: Multiplicative character sums on A^n\n (5.1) The general setting\n (5.2) First main theorem: the case when χ^e is nontrivial\n (5.3) Continuation of the proof of Theorem 5.2.2 for n = 1\n (5.4) Continuation of the proof of Theorem 5.2.2 for general n\n (5.5) Analysis of Gr^0(m(n, e, χ)), for e prime to p but χ^e = 1\n (5.6) Proof of Theorem 5.5.2 in the case n ≥ 2\nChapter 6: Middle additive convolution\n (6 .1 ) Middle convolution and its effect on local monodromy\n (6.2) Interlude: some galois theory in one variable\n (6.3) Proof of Theorem 6.2.11\n (6.4) Interpretation in terms of Swan conductors\n (6.5) Middle convolution and purity\n (6.6 ) Application to the monodromy of multiplicative character sums in several variables\n (6.7) Proof of Theorem 6.6.5, and applications\n (6.8) Application to the monodromy of additive character sums in several variables\nAppendix A6: Swan-minimal poles\n (A6.1) Swan conductors of direct images\n (A6.2) An application to Swan conductors of pullbacks\n (A6.3) Interpretation in terms of canonical extensions\n (A6.4) Belyi polynomials, non-canonical extensions, and hypergeometric sheaves\nChapter 7: Pullbacks to curves from A^1\n (7.1) The general pullback setting\n (7.2) General results on Ggeom for pullbacks\n (7.3) Application to pullback families of elliptic curves and of their symmetric powers\n (7.4) Cautionary examples\n (7.5) Appendix: Degeneration of Leray spectral sequences\nChapter 8: One variable twists on curves\n (8.1) Twist sheaves in the sense of [Ka-TLFM]\n (8.2) Monodromy of twist sheaves in the sense of [Ka-TLFM]\nChapter 9: Weierstrass sheaves as inputs\n (9.1) Weierstrass sheaves\n (9.2) The situation when 2 is invertible\n (9.3) Theorems of geometric irreducibility in odd characteristic\n (9.4) Geometric Irreducibility in even characteristic\nChapter 10: Weierstrass families\n (10.1) Universal Weierstrass families in arbitrary characteristic\n (10.2) Usual Weierstrass families in characteristic p ≥ 5\nChapter 11: FJTwist families and variants\n (11.1) (FJ, twist) families in characteristic p ≥ 5\n (11.2) (j^-1, twist) families in characteristic 3\n (11.3) (j^-1, twist) families in characteristic 2\n (11.4) End of the proof of 11.3.25: Proof that Ggeom contains a reflection\nChapter 12: Uniformity results\n (12.1) Fibrewise perversity: basic properties\n (12.2) Uniformity results for monodromy; the basic setting\n (12.3) The Uniformity Theorem\n (12.4) Applications of the Uniformity Theorem to twist sheaves\n (12.5) Applications to multiplicative character sums\n (12.6) Non-application (sic!) to additive character sums\n (12.7) Application to generalized Weierstrass families of elliptic curves\n (12.8) Application to usual Weierstrass families of elliptic curves\n (12.9) Application to FJTwist families of elliptic curves\n (12.10) Applications to pullback families of elliptic curves\n (12.11) Application to quadratic twist families of elliptic curves\nChapter 13: Average analytic rank and large N limits\n (13.1) The basic setting\n (13.2) Passage to the large N limit: general results\n (13.3) Application to generalized Weierstrass families of elliptic curves\n (13.4) Application to usual Weierbtrass families of elliptic curves\n (13.5) Applications to FJTwist families of elliptic curves\n (13.6) Applications to pullback families of elliptic curves\n (13.7) Applications to quadratic twist families of elliptic curves\nReferences\nNotation Index\nSubject Index