On L-adic Cohomology of Artin Stacks PDF Download
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Author: Shenghao Sun
Publisher:
ISBN:
Category :
Languages : en
Pages : 250
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Book Description
We develop the notion of stratifiability in the context of derived categories and the six operations for stacks in the work of Laszlo and Olsson. Then we reprove Behrend's Lefschetz trace formula for stacks, and give the meromorphic continuation of the L-series of stacks defined over a finite field. We give an upper bound for the weights of the cohomology groups of stacks, and as an application, prove the decomposition theorem for perverse sheaves on stacks with affine diagonal, both over finite fields and over the complex numbers. Along the way, we generalize the structure theorem of mixed sheaves and the generic base change theorem for stacks. We also give a short exposition on the lisse-analytic topoi of complex analytic stacks, and give a comparison between the lisse-etale topos of a complex algebraic stack and the lisse-analytic topos of its analytification.
Author: Shenghao Sun
Publisher:
ISBN:
Category :
Languages : en
Pages : 250
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Book Description
We develop the notion of stratifiability in the context of derived categories and the six operations for stacks in the work of Laszlo and Olsson. Then we reprove Behrend's Lefschetz trace formula for stacks, and give the meromorphic continuation of the L-series of stacks defined over a finite field. We give an upper bound for the weights of the cohomology groups of stacks, and as an application, prove the decomposition theorem for perverse sheaves on stacks with affine diagonal, both over finite fields and over the complex numbers. Along the way, we generalize the structure theorem of mixed sheaves and the generic base change theorem for stacks. We also give a short exposition on the lisse-analytic topoi of complex analytic stacks, and give a comparison between the lisse-etale topos of a complex algebraic stack and the lisse-analytic topos of its analytification.
Author: Kai Behrend
Publisher: American Mathematical Soc.
ISBN: 0821829297
Category : Mathematics
Languages : en
Pages : 110
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Book Description
This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.
Author: Martin C. Olsson
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 422
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Book Description
In this text the author uses stack-theoretic techniques to study the crystalline structure on the de Rham cohomology of a proper smooth scheme over a $p$-adic field and applications to $p$-adic Hodge theory. He develops a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks and applies it to the construction and study of the $(\varphi, N, G)$-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the $C_{\text {st}}$-conjecture using the method of Fontaine, Messing, Hyodo, Kato, and Tsuji, except for the key computation of $p$-adic vanishing cycles. He also generalizes the construction of the monodromy operator to schemes with more general types of reduction than semistable and proves new results about tameness of the action of Galois on cohomology.
Author: Dan Abramovich
Publisher: American Mathematical Soc.
ISBN: 0821847023
Category : Mathematics
Languages : en
Pages : 506
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Book Description
This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.
Author: Lei Fu
Publisher: World Scientific
ISBN: 9814464805
Category : Mathematics
Languages : en
Pages : 622
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Book Description
New Edition available hereEtale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.
Author: Martin Olsson
Publisher: American Mathematical Soc.
ISBN: 1470427982
Category : Mathematics
Languages : en
Pages : 313
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Book Description
This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
Author: Eberhard Freitag
Publisher: Springer Science & Business Media
ISBN: 3662025418
Category : Mathematics
Languages : en
Pages : 336
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Book Description
Some years ago a conference on l-adic cohomology in Oberwolfach was held with the aim of reaching an understanding of Deligne's proof of the Weil conjec tures. For the convenience of the speakers the present authors - who were also the organisers of that meeting - prepared short notes containing the central definitions and ideas of the proofs. The unexpected interest for these notes and the various suggestions to publish them encouraged us to work somewhat more on them and fill out the gaps. Our aim was to develop the theory in as self contained and as short a manner as possible. We intended especially to provide a complete introduction to etale and l-adic cohomology theory including the monodromy theory of Lefschetz pencils. Of course, all the central ideas are due to the people who created the theory, especially Grothendieck and Deligne. The main references are the SGA-notes [64-69]. With the kind permission of Professor J. A. Dieudonne we have included in the book that finally resulted his excellent notes on the history of the Weil conjectures, as a second introduction. Our original notes were written in German. However, we finally followed the recommendation made variously to publish the book in English. We had the good fortune that Professor W. Waterhouse and his wife Betty agreed to translate our manuscript. We want to thank them very warmly for their willing involvement in such a tedious task. We are very grateful to the staff of Springer-Verlag for their careful work.
Author: Jean-Pierre Serre
Publisher: CRC Press
ISBN: 1439863865
Category : Mathematics
Languages : en
Pages : 203
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Book Description
This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Author: Skip Garibaldi
Publisher: Springer Science & Business Media
ISBN: 1441962115
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.
Author: Michael Alan Rose
Publisher:
ISBN:
Category :
Languages : en
Pages : 100
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Book Description
