Results 1  10
of
26
Integral Canonical Models for Shimura Varieties of Preabelian Type
, 2003
"... We prove the existence of integral canonical models of Shimura varieties of preabelian type with respect to primes of characteristic at least 5. ..."
Abstract

Cited by 40 (22 self)
 Add to MetaCart
We prove the existence of integral canonical models of Shimura varieties of preabelian type with respect to primes of characteristic at least 5.
Manin problems for Shimura varieties of Hodge type
, 2007
"... Let k be a perfect field of characteristic p> 0. We prove the existence of ascending and descending slope filtrations for Shimura pdivisible objects over k. We use them to classify rationally these objects over ¯ k. Among geometric applications, we mention two. First we formulate Manin problems ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
Let k be a perfect field of characteristic p> 0. We prove the existence of ascending and descending slope filtrations for Shimura pdivisible objects over k. We use them to classify rationally these objects over ¯ k. Among geometric applications, we mention two. First we formulate Manin problems for Shimura varieties of Hodge type. Under two mild conditions (checked for p ≥3 in [45]) we solve them. Second we formulate integral Manin problems. We solve them for some Shimura varieties of PEL type.
CM lifts for Isogeny Classes of Shimura Fcrystals over Finite Fields
, 2007
"... We extend to large contexts pertaining to Shimura varieties of Hodge type a result of Zink on the existence of CM lifts to characteristic 0 of suitable representatives of certain isogeny classes of abelian varieties endowed with endomorphisms over finite fields. These contexts are general enough in ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
We extend to large contexts pertaining to Shimura varieties of Hodge type a result of Zink on the existence of CM lifts to characteristic 0 of suitable representatives of certain isogeny classes of abelian varieties endowed with endomorphisms over finite fields. These contexts are general enough in order to apply to the Langlands–Rapoport conjecture for all special fibres of characteristic at least 5 of integral canonical models of Shimura varieties of Hodge type.
A motivic conjecture of Milne
, 2007
"... Let k be an algebraically closed field of characteristic p> 0. Let W(k) be the ring of Witt vectors with coefficients in k. We prove a motivic conjecture of Milne that relates the étale cohomology with Zp coefficients to the crystalline cohomology with integral coefficients, in the wider context ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
Let k be an algebraically closed field of characteristic p> 0. Let W(k) be the ring of Witt vectors with coefficients in k. We prove a motivic conjecture of Milne that relates the étale cohomology with Zp coefficients to the crystalline cohomology with integral coefficients, in the wider context of pdivisible groups endowed with families of crystalline tensors over a finite, discrete valuation ring extension of W(k). The result implicitly extends work of Faltings. As a main new tool we construct global deformations of pdivisible groups endowed with crystalline tensors over certain regular, formally smooth schemes over W(k).
Shimura Varieties and Moduli
, 2011
"... Connected Shimura varieties are the quotients of hermitian symmetric domains by discrete groups defined by congruence conditions. We examine their relation with moduli varieties. ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Connected Shimura varieties are the quotients of hermitian symmetric domains by discrete groups defined by congruence conditions. We examine their relation with moduli varieties.
Sousvarietes des varietes de Shimura
, 2000
"... ne peut plus consciensieuse et mettent egalement une bonne ambiance. Meci a mon amie Katya et a mes parents pour leur soutien moral. 3 Notations et conventions 1. On note b Z := limproj n Z=nZ = Q p Z p le complete profini de Z. On note A f := b Z Q l'anneau des adeles finis et A := R ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
ne peut plus consciensieuse et mettent egalement une bonne ambiance. Meci a mon amie Katya et a mes parents pour leur soutien moral. 3 Notations et conventions 1. On note b Z := limproj n Z=nZ = Q p Z p le complete profini de Z. On note A f := b Z Q l'anneau des adeles finis et A := R A f l'anneau des adeles. 2. Par corps de nombres on entend une extension finie de Q . 3. On note Q la cloture algebrique de Q dans C . 4. On dit qu'un premier p decompose un corps de nombres F si F Q p est un produit de copies de Q p . 5. On ne suppose pas les varietes analytiques lisses. Par exemple
The Mumford–Tate Conjecture and Shimura Varieties, Part I
, 2002
"... We prove the Mumford–Tate conjecture for those abelian varieties over number fields whose extensions to C have attached adjoint Shimura pairs having all simple factors of certain Shimura types. In particular, we prove this conjecture for the orthogonal case (Bn and DR n Shimura types). As a main t ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
We prove the Mumford–Tate conjecture for those abelian varieties over number fields whose extensions to C have attached adjoint Shimura pairs having all simple factors of certain Shimura types. In particular, we prove this conjecture for the orthogonal case (Bn and DR n Shimura types). As a main tool, we construct embeddings of Shimura varieties (of whose adjoints are) of prescribed abelian type into unitary Shimura varieties of PEL type. We also use them to study integral models of these Shimura varieties. For instance, we prove the existence of integral canonical models of unitary Shimura varieties with respect to odd primes.
Canonical models of Shimura curves
, 2003
"... As an introduction to Shimura varieties, and, in particular, to Deligne’s Bourbaki and Corvallis talks (Deligne 1971, 1979), I explain the main ideas and results of the general theory of Shimura varieties in the context of Shimura curves. These notes had their origin in a twohour lecture I gave on ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
As an introduction to Shimura varieties, and, in particular, to Deligne’s Bourbaki and Corvallis talks (Deligne 1971, 1979), I explain the main ideas and results of the general theory of Shimura varieties in the context of Shimura curves. These notes had their origin in a twohour lecture I gave on September 10, 2002. They are available at www.jmilne.org/math/. Please send corrections and comments to me at