Rainer Weissauer's Books

Cohomological Tensor Functors on Representations of the General Linear Supergroup

By: Thorsten Heidersdorf,Rainer Weissauer

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Cohomological Tensor Functors on Representations of the General Linear Supergroup

By: Thorsten Heidersdorf,Rainer Weissauer

We define and study cohomological tensor functors from the category Tn of finite-dimensional representations of the supergroup Gl(n|n) into Tn−r for 0 < r ≤ n. In the case DS : Tn → Tn−1 we prove a formula DS(L) = ΠniLi for the image of an arbitrary irreducible representation. In particular DS(L) is semisimple and multiplicity free. We derive a few applications of this theorem such as the degeneration of certain spectral sequences and a formula for the modified superdimension of an irreducible representation.

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Page Count

106

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470447142

ISBN 13

9781470447144

Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds

By: Rainer Weissauer

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Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds

By: Rainer Weissauer

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder [40] and Laumon [62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I ?nally did not p- sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now available in [115]. Instead I tried to improve the presentation modestly, in particular by adding cross-references wherever I felt this was necessary. In addition, Chaps. 11 and 12 and Sects. 5. 1, 5. 4, and 5. 5 were added; these were written in 1998. I willgivea moredetailedoverviewofthecontentofthedifferentchaptersbelow. Before that I should mention that the two main results are the proof of Ramanujan’s conjecture for Siegel modular forms of genus 2 for forms which are not cuspidal representations associated with parabolic subgroups(CAP representations), and the study of the endoscopic lift for the group GSp(4). Both topics are formulated and proved in the ?rst ?ve chapters assuming the stabilization of the trace formula. All the remaining technical results, which are necessary to obtain the stabilized trace formula, are presented in the remaining chapters. Chapter 1 gathers results on the cohomology of Siegel modular threefolds that are used in later chapters, notably in Chap. 3. At the beginning of Chap.

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Page Count

384

Publisher

Springer

Published Date

ISBN 10

3540893067

ISBN 13

9783540893066

Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform

By: Reinhardt Kiehl,Rainer Weissauer

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Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform

By: Reinhardt Kiehl,Rainer Weissauer

The authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.

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