Moments, monodromy, and perversity : a diophantine perspective /
It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably ""pure"" algebro-geometric families of character sums over finite fields (and of their associated...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton :
Princeton University Press,
2005.
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| Series: | Annals of mathematics studies ;
no. 159. |
| Subjects: | |
| Online Access: | Connect to this title online (unlimited users allowed) |
Table of Contents:
- Cover; Title; Copyright; Contents; Introduction; Chapter 1: Basic results on perversity and higher moments; (1.1) The notion of a d-separating space of functions; (1.2) Review of semiperversity and perversity; (1.3) A twisting construction: the object Twist(L, K, F, h); (1.4) The basic theorem and its consequences; (1.5) Review of weights; (1.6) Remarks on the various notions of mixedness; (1.7) The Orthogonality Theorem; (1.8) First Applications of the Orthogonality Theorem; (1.9) Questions of autoduality: the Frobenius-Schur indicator theorem
- (1.10) Dividing out the ""constant part"" of an ɩ-pure perverse sheaf(1.11) The subsheaf Nncst0 in the mixed case; (1.12) Interlude: abstract trace functions; approximate trace functions; (1.13) Two uniqueness theorems; (1.14) The central normalization F0 of a trace function F; (1.15) First applications to the objects Twist(L,K,F,h): The notion of standard input; (1.16) Review of higher moments; (1.17) Higher moments for geometrically irreducible lisse sheaves; (1.18) Higher moments for geometrically irreducible perverse sheaves; (1.19) A fundamental inequality
- (1.20) Higher moment estimates for Twist(L, K, F, h)(1.21) Proof of the Higher Moment Theorem 1.20.2: combinatorial preliminaries; (1.22) Variations on the Higher Moment Theorem; (1.23) Counterexamples; Chapter 2: How to apply the results of Chapter 1; (2.1) How to apply the Higher Moment Theorem; (2.2) Larsen's Alternative; (2.3) Larsen's Eighth Moment Conjecture; (2.4) Remarks on Larsen's Eighth Moment Conjecture; (2.5) How to apply Larsen's Eighth Moment Conjecture; its current status; (2.6) Other tools to rule out finiteness of Ggeom; (2.7) Some conjectures on drops