Scholarly Works - Book sections
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January 1, 2012
Thus far we have ignored classes in (Formula presented.) and their Poincaré duals in intersection homology. We now take up the study of these classes. ...
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January 1, 2012
In this chapter we collect some known facts on Hilbert modular forms and varieties, mostly for the purpose of fixing our notation. These concepts will be used in Chapter 7, where we will recall the description of the intersection cohomology of Hilbert modu ...
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January 1, 2012
We use the same setup as in the previous chapter: L/E is a quadratic extension of totally real fields Gal(L/E) = 〈1, ς〉 Gal(L/E)^ = 〈1, η〉, c ⊂ OL is an ideal, and n:=[L:Q], d:=dL/E, D := DL/E cE := c∩OE
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January 1, 2012
In this section we begin with the general theory of local systems, automorphic vector bundles, and automorphy factors. After describing the finite-dimensional representation theory of GL2 we determine the explicit equations relating modular form ...
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January 1, 2012
Recall (e.g.,[Hud ]) that a closed convex linear cell is the convex hull of finitely many points in Euclidean space. A convex linear cell complex K is a finite collection of closed convex linear cells in some ℝN such that if σ ∈ K then every fac ...
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January 1, 2012
In this chapter we use Proposition 6.6 to construct a map Hilbert modular forms ⟶ intersection cohomology which takes weight, nebentypus ⟶ local coefficient system Hecke operator ⟶ action of Hecke correspondence Petersson product ⟶ intersection product. ...
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January 1, 2012
In this chapter we consider a quadratic extension L/E of totally real fields. The inclusion E → L gives rise to Hilbert modular subvarieties, known as Hirzebruch-Zagier cycles, Z ⊂ Y with dim(Y ) = 2 dim(Z). ...
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January 1, 2012
In their seminal paper [Hirz] on the intersection theory of Hilbert modular surfaces, F. Hirzebruch and D. Zagier mentioned that the motivation for their work was to explain an observation of J.-P. Serre. ...
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January 1, 2012
In this chapter we recall the relation between intersection homology,constructed using (p, i)-allowable chains as in [Gre4],an d intersection cohomology, constructed via sheaf theory. ...
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January 1, 2012
Possible references for the geometry described in this section include [BoS,Sa2, Gre6,Gr e3,Gr e2]. ...
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January 1, 2012
The goal of this chapter is to prove Theorems 8.4 and 8.5,t he full versions of Theorems 1.1 and 1.2 given in the introduction. We consider a quadratic extension of totally real number fields L/E. ...
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