CONTENTS

Abstract

Introduction

PART I. Preparations

A. Statement of Theorem

B. Stable conjugacy

C. Explicit representatives

D. Stable 0-conjugacy

E. Useful facts

F. Endoscopic groups

G. Instability

H. Kazhdan's decomposition

I. Decompositions for GL(2)

J. Decomposition for Sp(2)

PART II. Main comparison

A. Strategy

B. Twisted orbital integrals of type (I)

C. Orbital integrals of type (I)

D. Comparison in stable case (I), E/F unramified

E. Comparison in stable case (I), E/F ramified

F. Endoscopy for H = GSp{2), type (I)

Unstable twisted case. Twisted endoscopic group of type I.F.2

Twisted endoscopic group of type I.F.3, E/F unramified

G. Twisted orbital integrals of type (II)

H. Orbital integrals of type (II)

I. Comparison in case (II), E/E3 ramified (e = 2)

Unstable twisted case. Twisted endoscopic group of type I.F.2

J. Comparison in case (II), E/E3 unramified (e = 1)

Unstable twisted case. Twisted endoscopic group of type I.F.3

K. Endoscopy for GSp(2), type (II)

L. Comparison in case (III)

Unstable twisted case. Twisted endoscopic group of type I.F.2

M. Comparison in case (IV)

Unstable twisted case. Twisted endoscopic group of type I.F.2

PART III. Semi simple reduction

A. Review

B. Case of torus of type (I)

C. Case of torus of type (II)

D. Case of torus of type (III)

E. Case of torus of type (IV)

References

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