Download Drinfeld Moduli Schemes and Automorphic Forms: The Theory of by Yuval Z Flicker PDF

By Yuval Z Flicker

Drinfeld Moduli Schemes and Automorphic types: the speculation of Elliptic Modules with functions is predicated at the author’s unique paintings setting up the correspondence among ell-adic rank r Galois representations and automorphic representations of GL(r) over a functionality box, within the neighborhood case, and, within the worldwide case, below a restrict at a unmarried position. It develops Drinfeld’s concept of elliptic modules, their moduli schemes and overlaying schemes, the easy hint formulation, the mounted element formulation, in addition to the congruence family members and a "simple" speak theorem, now not but released anyplace. This model, in accordance with a up to date direction taught by means of the writer on the Ohio nation college, is up to date with references to analyze that has prolonged and built the unique paintings. using the speculation of elliptic modules within the current paintings makes it available to graduate scholars, and it'll function a beneficial source to facilitate an front to this interesting sector of mathematics.

Table of Contents

Cover

Drinfeld Moduli Schemes and Automorphic varieties - the speculation of Elliptic Modules with Applications

ISBN 9781461458876 ISBN 9781461458883

Contents

1. Introduction

Part 1. Elliptic Moduli

2. Elliptic Modules: Analytic Definition
three. Elliptic Modules: Algebraic Definition
four. Elliptic Modules: Geometric Definition
five. masking Schemes

Part 2. Hecke Correspondences

6. Deligne's Conjecture and Congruence Relations

Part three. hint Formulae

7. Isogeny Classes
eight. Counting Points
nine. round Functions

Part four. greater Reciprocity Laws

10. Purity Theorem
eleven. lifestyles Theorem
12. Representations of a Weil Group
thirteen. basic communicate Theorem

References

Index

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Extra info for Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications

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Hence ϕ is a standard elliptic module. If P is an endomorphism of ϕ and Spec B is connected, then it follows from (ii) that there is a nonnegative integer s such that P is strictly of degree s. If P is invertible then s = 0 and P is linear. The proposition follows. Let I = 0 be an ideal in A. Let E = Eϕ be an elliptic functor of rank r over S. 3. Let EI = Ann I|E be the subfunctor of E annihilated by I. 5. The annihilator EI of I in E is finite and flat as an affine group scheme over S. Proof. Up to isomorphism we may assume that E = Eϕ is a standard elliptic functor.

1. Let K be a field of characteristic p > 0. Let n be a positive integer with (p, n) = 1. Let X = Y be the affine group scheme Gm,K = Spec K[x, x−1 ]. Then the morphism Y → X defined by x → xn is ´etale, since (n, p) = 1, and we obtain a locally constant sheaf YX on X´et . Z. 1007/978-1-4614-5888-3 6, © Yuval Z. Flicker 2013 45 46 YUVAL Z. FLICKER group of nth roots of unity in the multiplicative group K × of K. We claim that the restriction of YX to the ´etale covering {Z → X} = {Y → X} of X is the constant sheaf defined by N .

8, p. 358) it follows that one has the canonical isomorphisms (Ri b! L)s = Hci (Xs , L|Xs )and(Ri b! L)v = Hci (Xv , L|Xv ). 2. 7. Let f, h : X → X be finite morphisms, and b : X → S a morphism where S is irreducible. Let L be a smooth sheaf on X, and fix a morphism α : h∗ L → f ! L.

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