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Introduction

Dennis Gaitsgory and Jacob Lurie

in Weil's Conjecture for Function Fields: Volume I (AMS-199)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691182148
eISBN:
9780691184432
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691182148.003.0001
Subject:
Mathematics, Mathematical Finance

This introductory chapter sets out the book's purpose, which is to study Weil's conjecture over function fields: that is, fields K which arise as rational functions on an algebraic curve X over a ... More


Weil's Conjecture for Function Fields: Volume I (AMS-199)

Dennis Gaitsgory and Jacob Lurie

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691182148
eISBN:
9780691184432
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691182148.001.0001
Subject:
Mathematics, Mathematical Finance

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at ... More


The Formalism of l-adic Sheaves

Dennis Gaitsgory and Jacob Lurie

in Weil's Conjecture for Function Fields: Volume I (AMS-199)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691182148
eISBN:
9780691184432
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691182148.003.0002
Subject:
Mathematics, Mathematical Finance

The ℓ-adic product formula discussed in Chapter 4 will need to make use of analogous structures, which are simply not visible at the level of the triangulated category Dℓ(X). This chapter attempts to ... More


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