Bibliography of Nicholas M. Katz
C.V. of Nicholas M. Katz
Photo from 60'th Birthday Conference
Photo from 60'th Birthday Conference (high resolution version)
V-Strom DL650 suspension adjustment
fans of MONODROMY.COM can find most of it at its new home
Some older work can be found HERE (listed alphabetically by title)
recent work is below (most recent first)
(joint with Pham Huu Tiep)Airy sheaves of Laurent type: an
introduction
(joint with Pham Huu Tiep) On some Airy sheaves of Laurent type
(joint with Pham Huu Tiep)Moments, exponential sums, and monodromy
groups
(joint with Pham Huu Tiep) Condition (S+) in ranks 4,8, and 9
(joint with Pham Huu Tiep)Exponential Sums, Hypergeometric Sheaves,
and Monodromy Groups
Some open questions about curves and abelian varieties over
finite fields
Erratum to "Nilpotent Connections and the Monodromy Theorem"
(joint with Antonio Rojas-Leon and Pham Huu Tiep)Rigid Local Systems
and Sporadic Simple Groups
(joint with Levent Alpoge,Gabriel Navarro, E.A. O'Brien, and Pham Huu
Tiep) Local Systems and Suzuki Groups (published version)
Exponential Sums and Finite Groups(slides of talk at Luc Illusie
81 conference)
(joint with Pham Huu Tiep)Hypergeometric Sheaves and Finite
Symplectic and Unitary Groups
(joint with Pham Huu Tiep) Exponential sums and total Weil
representations of finite symplectic and unitary groups
(joint with Pham Huu Tiep)MONODROMY GROUPS OF KLOOSTERMAN AND
HYPERGEOMETRIC SHEAVES
(joint with Pham Huu Tiep)Corrections to MONODROMY GROUPS OF
KLOOSTERMAN AND
HYPERGEOMETRIC SHEAVES (joint with Pham Huu Tiep) Rigid local systems and finite general
linear groups
(joint with Pham Huu Tiep)Moments of Weil representations of finite
special unitary groups
(joint with Antonio Rojas Leon and Pham Huu Tiep)A rigid local system
with monodromy group the big Conway group 2.Co_1, and two others with
monodromy group the Suzuki group 6.Suz
(joint with Antonio Rojas Leon and Pham Huu Tiep) Rigid local
systems
with monodromy group the Conway group Co_2 (joint with Antonio Rojas Leon and Pham Huu Tiep) Rigid local systems
with monodromy group the Conway group Co_3
(joint with Antonio Rojas Leon) A rigid local system with monodromy
group 2.J_2
How hard is it to be ordinary? (slides of talk at Loeser 60
conference)
(joint with Pham Huu Tiep) Rigid local systems,moments, and finite
unitary groups
(joint with Pham Huu Tiep)Local systems and finite unitary and
symplectic groups
(joint with Pham Huu Tiep) Rigid local systems and finite symplectic
groups
A note on galois representations with big image
Rigid Local Systems and Alternating Groups (joint with Guralnick and
Tiep), to appear in Tunisian Journal of Mathematics
Exponential Sums, Ree Groups and Suzuki Groups:Conjectures
Rigid local systems on \A^1 with finite monodromy (with an appendix
by Pham Huu Tiep) to appear in Mathematika
G_2 and some exceptional Witt vector identities
Witt Vectors and a Question of Rudnick and Waxman
A note on Random matrix integrals, moment identities, and Catalan
numbers
Searching for thin groups (slides of talk at Sarnak Birthday
conference)
On a question of Rudnick: do we have square root cancellation for
error terms in moment calculations?
ON TWO QUESTIONS OF ENTIN, KEATING, AND RUDNICK ON PRIMITIVE
DIRICHLET CHARACTERS
WITT VECTORS AND A QUESTION OF ENTIN,KEATING, AND RUDNICK
Equidistribution questions arising from universal
extensions(published version)
Wieferich past and future
A note on RH for curves and hypersurfaces over finite fields(typo's
corrected Jan. 7, 2014)
Sato-Tate in the higher dimensional case: elaboration of 9.5.4 in
Serre's N_X(p) book
On a question of Zannier
Elliptic convolution, G_2, and elliptic surfaces
Simple Things We Don't Know
On the graph attached to truncated big Witt vectors (Warning to the
Reader, explaining relation to work of S.D.Cohen, added March 14, 2012)
Witt vectors and a question of Keating and Rudnick(to appear in IMRN)
On a question of Keating and Rudnick about primitive Dirichlet
characters with squarefree conductor(new longer title: to appear in
IMRN)
Rigid Local Systems and a Problem of Wootters(typo's corrected Sept.
2012)
Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field
Mellin Transforms(new title, now in book form,
updated July 14, 2011)
2,3,5, Legendre:\pm Trace ratios in families of elliptic curves
(typo's corrected August 18, 2010)
(joint with Guralnick and Harris) Automorphic realization of residual
Galois representations
Lang-Trotter revisited (published version)
(joint with Bombieri)A Note on Lower Bounds for Frobenius
Traces(revised Sept. 10, 2009)
(joint with Dettweiler) Appendix: On Galois Representations with
values in G_2 (appendix to a paper of Dettweiler and Reiter, to appear
in Compositio)
From Clausen to Carlitz: low-dimensional spin groups and identities
among character sums
Estimates for nonsingular mixed character sums (Thm. 3.1 improved Feb
19,2007, Appendix added and typo's corrected Feb. 24, more typo's fixed
Aug 11, 2007)
On a question of Bombieri and Bourgain(version of July 14, 2008; to
appear in
Forum Mathematicum)
Another look at the Dwork family (revised Feb.4,2007; adds App.
III,corrects more typo's)
Estimates for mixed character sums (to appear in GAFA)
On a question of Browning and Heath-Brown
Appendix: Lefschetz pencils with imposed subvarieties
Report on the irreducibility of L-functions (to appear in Lang
memorial volume)
E-polynomials, zeta-equivalence, and polynomial-count varieties
(appendix to a paper of Rodriguez-Villegas and Hausel)
G_2 and hypergeometric sheaves (corrections to 10.1,10.2 added June
11,2008, correction to 9.1 added January 24, 2016)
Corrections to "G_2 and hypergeometric sheaves" (as of January 42,
2016)
On a question of Lillian Pierce
Hooley parameters for families of exponential sums over finite fields
Notes on G_2, determinants, and equidistribution (typo's corrected
Dec. 9, 2003)
(joint with Esnault) Cohomological divisibility and point count
divisibility (corrected version of nov. 10, 2003)
Corrected version of Chapter 5 of "Twisted L-Functions and Monodromy"
Moments, Monodromy, and Perversity: a Diophantine Perspective
Space filling curves over finite fields (see corrections below)
Corrections to "Space filling curves over finite fields"
(joint with Pandharipande) Inequalities related to Lefschetz pencils
and integrals of Chern classes
(joint with Fouvry) A general stratification theorem for exponential
sums, and applications
Estimates for "nonsingular" multiplicative character sums
A semicontinuity result for monodromy under degeneration
Sato-Tate Equidistribution of Kurlberg-Rudnick Sums
AWS2000 Lectures: L -functions and monodromy: four lectures on Weil II
Larsen's Alternative, Moments, and the Monodromy of Lefschetz Pencils
Sums of Betti numbers in arbitrary characteristic
Frobenius-Schur indicator & the ubiquity of Brock-Granville Quadratic Excess
Twisted L-Functions and Monodromy (whole book)
Twisted L-Functions and Monodromy (introduction only)
(joint with de Jong) Monodromy and the Tate Conjecture:Picard numbers and Mordell-Weil ranks in families
Estimates for "singular" exponential sums
(joint with Tate) Bernard Dwork (1923-1998)
manuscript of Rigid Local Systems, with corrections
Corrections to Rigid Local Systems
manuscript of Exponential Sums and Differential Equations, with corrections
Corrections to Exponential Sums and Differential Equations
scan of Katz-Mazur (now searchable; downloads but does not open in Safari)
Corrected version of 6.16.6 in Katz-Sarnak
Katz-Sarnak the book, blurry but searchable
Katz,Sommes Exponentielles, blurry but searchable
Subject index to Katz-Sarnak
Notation index to Katz-Sarnak
Katz, Gauss Sums, Kloosterman Sums, and Monodromy