Results 1  10
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14
Foliations in Moduli Spaces of Abelian Varieties
 Journ. Amer. Math. Soc
, 2002
"... In this paper we study abelian varieties and of pdivisible groups in characteristic p. Even though a nontrivial deformation... ..."
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Cited by 85 (21 self)
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In this paper we study abelian varieties and of pdivisible groups in characteristic p. Even though a nontrivial deformation...
Hypersymmetric Abelian Varieties
, 2006
"... We introduce the notion of a hypersymmetric abelian variety over a field of positive characteristic p. We show that every symmetric Newton polygon admits a hypersymmetric abelian variety having that Newton polygon; see 2.5 and 4.8. Isogeny classes of absolutely simple hypersymmetric abelian variet ..."
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Cited by 23 (13 self)
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We introduce the notion of a hypersymmetric abelian variety over a field of positive characteristic p. We show that every symmetric Newton polygon admits a hypersymmetric abelian variety having that Newton polygon; see 2.5 and 4.8. Isogeny classes of absolutely simple hypersymmetric abelian varieties are classified in terms of their endomorphism algebras and Newton polygons. We also discuss connections with abelian varieties of PELtype, i.e. abelian varieties with extra symmetries, especially abelian varieties with real multiplications.
Moduli of abelian varieties
, 2010
"... We start with a discussion of CM abelian varieties in characteristic zero, and in positive characteristic. An abelian variety over a finite field is a CM abelian variety, as Tate proved. Can it be CMlifted to characteristic zero? Does there exist an abelian variety, say over Q a, or over Fp, of d ..."
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Cited by 13 (8 self)
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We start with a discussion of CM abelian varieties in characteristic zero, and in positive characteristic. An abelian variety over a finite field is a CM abelian variety, as Tate proved. Can it be CMlifted to characteristic zero? Does there exist an abelian variety, say over Q a, or over Fp, of dimension g> 3 not isogenous with the Jacobian of an algebraic curve? Can we construct algebraic curves, say over C, where the Jacobian is a CM abelian variety? We give (partial) answers to these questions. Next we discuss stratifications and foliations of moduli spaces of abelian varieties in positive characteristic.
METHODS FOR pADIC MONODROMY
, 2008
"... We explain three methods for showing that the padic monodromy of a modular family of abelian varieties is ‘as large as possible’, and illustrate them in the case of the ordinary locus of the moduli space of gdimensional principally polarized abelian varieties over a field of characteristic p. The ..."
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Cited by 7 (2 self)
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We explain three methods for showing that the padic monodromy of a modular family of abelian varieties is ‘as large as possible’, and illustrate them in the case of the ordinary locus of the moduli space of gdimensional principally polarized abelian varieties over a field of characteristic p. The first method originated from Ribet’s proof of the irreducibility of the Igusa tower for Hilbert modular varieties. The second and third methods both exploit Hecke correspondences near a hypersymmetric point, but in slightly different ways. The third method was inspired by work of Hida, plus a group theoretic argument for the maximality of ℓadic monodromy with ℓ ̸ = p.
On hypersymmetric abelian varieties
 Department of Mathematics Mathematisch Instituut University of Pennsylvania
"... The five years I spent in the graduate study has changed me a lot. Suddenly I feel that I am no longer asleep in my dearest dream. Burdens and responsibilities drop on my shoulders. Had no care and help from my wife Lei, I would not know where to go. I dedicate this thesis to her. This thesis is fin ..."
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Cited by 1 (0 self)
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The five years I spent in the graduate study has changed me a lot. Suddenly I feel that I am no longer asleep in my dearest dream. Burdens and responsibilities drop on my shoulders. Had no care and help from my wife Lei, I would not know where to go. I dedicate this thesis to her. This thesis is finished under the supervision of my advisor ChingLi Chai. I admire his pure spirit and I thank heartily for his patient and constant support. I have been a dear student of all the mathematicians of the Univerisity of Pennsylvania, to whom I thank from the bottom of my heart. I thank in particular the encouragement and support of Ted Chinburg. I am grateful to Professors Paula Tretkoff and Steven Zucker; they gave me as much support as they can when I met difficulties.
ChingLi Chai∗
"... Hecke orbits as Shimura varieties in positive characteristic ..."
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