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Localglobal compatibility and the action of monodromy on nearby cycles
 Duke Mathematical Journal
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters.
The Iwasawa main conjectures for GL2
, 2010
"... In this paper we prove the IwasawaGreenberg Main Conjecture for a large class of elliptic curves and modular forms. 1.1. The IwasawaGreenberg Main Conjecture. Let p be an odd prime. Let Q ⊂ C be the algebraic closure of Q in C. We fix an embedding Q ↩ → Q p. For simplicity we ..."
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In this paper we prove the IwasawaGreenberg Main Conjecture for a large class of elliptic curves and modular forms. 1.1. The IwasawaGreenberg Main Conjecture. Let p be an odd prime. Let Q ⊂ C be the algebraic closure of Q in C. We fix an embedding Q ↩ → Q p. For simplicity we
On the rigid cohomology of certain Shimura varieties. Preprint. Available at http://arxiv.org/abs/1411.6717
"... Abstract. We construct the compatible system of ladic representations associated to a regular algebraic cuspidal automorphic representation of GLn over a CM (or totally real) field and check localglobal compatibility for the ladic representation away from l and finite number of rational primes a ..."
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Abstract. We construct the compatible system of ladic representations associated to a regular algebraic cuspidal automorphic representation of GLn over a CM (or totally real) field and check localglobal compatibility for the ladic representation away from l and finite number of rational primes above which the CM field or the automorphic representation ramify. The main innovation is that we impose no selfduality hypothesis on the automorphic representation.
Vanishing theorems for torsion automorphic sheaves on compact PELtype Shimura varieties
, 2010
"... Given a compact PELtype Shimura variety, a sufficiently regular weight (defined by mild and effective conditions), and a prime number p unramified in the linear data and larger than an effective bound given by the weight, we show that the étale cohomology with Zpcoefficients of the given weight v ..."
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Cited by 8 (1 self)
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Given a compact PELtype Shimura variety, a sufficiently regular weight (defined by mild and effective conditions), and a prime number p unramified in the linear data and larger than an effective bound given by the weight, we show that the étale cohomology with Zpcoefficients of the given weight vanishes away from the middle degree, and hence has no ptorsion. We do not need any other assumption (such as ones on the images of the associated Galois representations).
Irreducibility of the Igusa tower
"... Fix a prime p. In [H06a], we have shown that the geometric automorphism group of the irreducible component of the mod p Shimura variety of PEL type (of level away from p) associated to a reductive group G of unitary and symplectic type is almost identical to G1(A (p∞) ) modulo global center (cf. Lem ..."
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Cited by 7 (5 self)
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Fix a prime p. In [H06a], we have shown that the geometric automorphism group of the irreducible component of the mod p Shimura variety of PEL type (of level away from p) associated to a reductive group G of unitary and symplectic type is almost identical to G1(A (p∞) ) modulo global center (cf. Lemma 1.1). Here G1 is the derived subgroup of G. In this paper, we give a (basically) characteristic p proof of the irreducibility of the Igusa tower over a reduction modulo p of the Shimura variety by showing that the stabilizer of an irreducible component of the tower is as large as possible under the PEL data. This is a characteristic pversion of the proof given in [PAF] Section 8.4 where we used mixedcharacteristic results to show the maximality of the stabilizer. Here is a general axiomatic approach to prove the irreducibility of an étale covering π: Ig → S of an irreducible variety S over an algebraically closed residue field F. Suppose the following two axioms: (A1) A group G = M1×G1 acts on Ig and S compatibly so that M1 ⊂ Aut(Ig/S), G1 ⊂ Aut(S) and G1 acts trivially on π0(Ig).
ON THE COHOMOLOGY OF COMPACT UNITARY GROUP SHIMURA VARIETIES AT RAMIFIED SPLIT PLACES
, 2012
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K.: Integral canonical models for Spin Shimura varieties, available at http://arxiv.org/pdf/1212.1243.pdf
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