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) |
MARC
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| 100 | 1 | |a Katz, Nicholas M., |d 1943- |1 https://id.oclc.org/worldcat/entity/E39PBJwxGkxqJwQFTRgKfm4pfq | |
| 245 | 1 | 0 | |a Moments, monodromy, and perversity : |b a diophantine perspective / |c Nicholas M. Katz. |
| 260 | |a Princeton : |b Princeton University Press, |c 2005. | ||
| 300 | |a 1 online resource (viii, 475 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 159 | |
| 504 | |a Includes bibliographical references (pages 455-460) and indexes. | ||
| 505 | 0 | |6 880-01 |a 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 | |
| 505 | 8 | |a (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 | |
| 505 | 8 | |a (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 | |
| 520 | |a 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 L-functions). Roughly speaking, Deligne showed that any such family obeys a ""generalized Sato-Tate law, "" and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the ""geometric monodromy | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Monodromy groups. | |
| 650 | 0 | |a Sheaf theory. | |
| 650 | 0 | |a L-functions. | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a L-functions |2 fast | |
| 650 | 7 | |a Monodromy groups |2 fast | |
| 650 | 7 | |a Sheaf theory |2 fast | |
| 776 | 0 | 8 | |i Print version: |z 9781400826957 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 159. | |
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| 880 | 8 | |6 505-00/(S |a (2.8) More tools to rule out finiteness of Ggeom: sheaves of perverse origin and their monodromyChapter 3: Additive character sums on A^n; (3.1) The theorem; (3.2) Proof of the LΨ Theorem 3.1.2; (3.3) Interlude: the homothety contraction method; (3.4) Return to the proof of the LΨ theorem; (3.5) Monodromy of exponential sums of Deligne type on A^n; (3.6) Interlude: an exponential sum calculation; (3.7) Interlude: separation of variables; (3.8) Return to the monodromy of exponential sums of Deligne type on A^n; (3.9) Application to Deligne polynomials | |
| 880 | 8 | |6 505-01/(S |a (3.10) Self dual families of Deligne polynomials(3.11) Proofs of the theorems on self dual families; (3.12) Proof of Theorem 3.10.7; (3.13) Proof of Theorem 3.10.9; Chapter 4: Additive character sums on more general X; (4.1) The general setting; (4.2) The perverse sheaf M(X, r, Zi's, ei's, Ψ) on P(e1 ..., er); (4.3) Interlude An exponential sum identity; (4.4) Return to the proof of Theorem 4.2.12; (4.5) The subcases n = 1 and n = 2; Chapter 5: Multiplicative character sums on A^n; (5.1) The general setting; (5.2) First main theorem: the case when χ^e is nontrivial | |
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