Supersingular abelian varieties over finite fields.
Berkeley thesis (advisor:
Hendrik W. Lenstra, Jr). See the two papers below.
[ps|pdf]Group
structures of supersingular abelian varieties over finite fields. J. Number Theory, 81 (2000), 292--309.
[ps|pdf]Supersingular
abelian varieties over finite fields. J. Number Theory, 86 (2001), 61--77.
[ps|pdf]On
the existence of absolutely simple abelian varieties of a given
dimension over an arbitrary field (joint with Everett W. Howe ). J. Number Theory, 92 (2002), 139--163.
[ps|pdf]Hyperelliptic
curves in characteristic 2(joint with Jasper Scholten). Inter. Math. Research Notices,17 (2002), 905--917.
[ps|pdf]First
slope case of
Wan's conjecture (joint with Jasper Scholten). Finite Fields and their Appl.8 (2002), 414--419.
[ps|pdf]Families
of supersingular curves in characteristic 2(joint with Jasper
Scholten). Mathematical Research Letters9 (2002), no. 5-6,
639--650.
[ps|pdf]p-adic
variation of L functions of one variable exponential sums, I. American Journal of Mathematics125 (2003), 669-690.
[ps|pdf]Slope
estimates on Artin-Schreier curves(joint with Jasper
Scholten). Compositio Math.137 (2003), 275--292. (misprints for the paper in print.)
[ps| pdf]The abc
conjecture and correctly rounded reciprocal square roots.(joint
with Ernie Croot
and Ren-Cang Li).
Theoretical Computer Science 315
(2004), Issues 2-3, 405--417.
(Special issue on Algebraic and
Numerical Algorithms, edited by I.Emiris, B.Mourrain and V.Pan.)
[ps|pdf]Asymptotic
variation of L functions of one-variable exponential sums. J. Reine Angew. Math., 572
(2004), 219--233.
[pdf]Construction
of some families of 2-dimensional crystalline representations.(joint
with Laurent Berger and Hanfeng Li). Mathematische Annalen329
(2004), no.2, 365--377.
[ps|pdf]
L-functions of exponential sums over one-dimensional
affinoids : Newton over Hodge. Inter. Math. Research Notices. 2004, no 30, (2004), 1529--1550.
[ps|pdf]Zeta functions of totally ramified p-covers of the
projective
line(joint with Hanfeng Li). Rend.
Sem. Mat. Univ. Padova113 (2005),
203--225.
[ps|pdf]
Hyperelliptic curves over F_2 of every 2-rank without extra
automorphisms. Proc. Amer. Math. Soc. 134 (2006), 323--331 .