Hardcover ISBN:  9781470435783 
Product Code:  PSPUM/97.2 
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eBook ISBN:  9781470446802 
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Hardcover ISBN:  9781470435783 
eBook: ISBN:  9781470446802 
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Hardcover ISBN:  9781470435783 
Product Code:  PSPUM/97.2 
List Price:  $139.00 
MAA Member Price:  $125.10 
AMS Member Price:  $111.20 
eBook ISBN:  9781470446802 
Product Code:  PSPUM/97.2.E 
List Price:  $135.00 
AMS Member Price:  $108.00 
Hardcover ISBN:  9781470435783 
eBook ISBN:  9781470446802 
Product Code:  PSPUM/97.2.B 
List Price:  $274.00 $206.50 
MAA Member Price:  $185.85 
AMS Member Price:  $219.20 $165.20 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 97; 2018; 635 ppMSC: Primary 14; 53;
This is Part 2 of a twovolume set.
Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments.
The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic.
Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic \(p\) and \(p\)adic tools, etc. The resulting articles will be important references in these areas for years to come.
ReadershipGraduate students and researchers working in algebraic geometry and its applications.
This item is also available as part of a set: 
Table of Contents

Part 2

David BenZvi and David Nadler  Betti Geometric Langlands

Bhargav Bhatt  Specializing varieties and their cohomology from characteristic $0$ to characteristic $p$

T. D. Browning  How often does the Hasse principle hold?

Lucia Caporaso  Tropical methods in the moduli theory of algebraic curves

Renzo Cavalieri, Paul Johnson, Hannah Markwig and Dhruv Ranganathan  A graphical interface for the GromovWitten theory of curves

Hélène Esnault  Some fundamental groups in arithmetic geometry

Laurent Fargues  From local class field to the curve and vice versa

Mark Gross and Bernd Siebert  Intrinsic mirror symmetry and punctured GromovWitten invariants

Eric Katz, Joseph Rabinoff and David ZureickBrown  Diophantine and tropical geometry, and uniformity of rational points on curves

Kiran S. Kedlaya and Jonathan Pottharst  On categories of $(\varphi , \Gamma )$modules

Minhyong Kim  Principal bundles and reciprocity laws in number theory

B. Klingler, E. Ullmo and A. Yafaev  Bialgebraic geometry and the AndréOort conjecture

Max Lieblich  Moduli of sheaves: A modern primer

Johannes Nicaise  Geometric invariants for nonarchimedean semialgebraic sets

Tony Pantev and Gabriele Vezzosi  Symplectic and Poisson derived geometry and deformation quantization

Alena Pirutka  Varieties that are not stably rational, zerocycles and unramified cohomology

Takeshi Saito  On the proper pushforward of the characteristic cycle of a constructible sheaf

Tamás Szamuely and Gergely Zábrádi  The $p$adic Hodge decomposition according to Beilinson

Akio Tamagawa  Specialization of $\ell $adic representations of arithmetic fundamental groups and applications to arithmetic of abelian varieties

Olivier Wittenberg  Rational points and zerocycles on rationally connected varieties over number fields


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This is Part 2 of a twovolume set.
Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments.
The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic.
Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic \(p\) and \(p\)adic tools, etc. The resulting articles will be important references in these areas for years to come.
Graduate students and researchers working in algebraic geometry and its applications.

Part 2

David BenZvi and David Nadler  Betti Geometric Langlands

Bhargav Bhatt  Specializing varieties and their cohomology from characteristic $0$ to characteristic $p$

T. D. Browning  How often does the Hasse principle hold?

Lucia Caporaso  Tropical methods in the moduli theory of algebraic curves

Renzo Cavalieri, Paul Johnson, Hannah Markwig and Dhruv Ranganathan  A graphical interface for the GromovWitten theory of curves

Hélène Esnault  Some fundamental groups in arithmetic geometry

Laurent Fargues  From local class field to the curve and vice versa

Mark Gross and Bernd Siebert  Intrinsic mirror symmetry and punctured GromovWitten invariants

Eric Katz, Joseph Rabinoff and David ZureickBrown  Diophantine and tropical geometry, and uniformity of rational points on curves

Kiran S. Kedlaya and Jonathan Pottharst  On categories of $(\varphi , \Gamma )$modules

Minhyong Kim  Principal bundles and reciprocity laws in number theory

B. Klingler, E. Ullmo and A. Yafaev  Bialgebraic geometry and the AndréOort conjecture

Max Lieblich  Moduli of sheaves: A modern primer

Johannes Nicaise  Geometric invariants for nonarchimedean semialgebraic sets

Tony Pantev and Gabriele Vezzosi  Symplectic and Poisson derived geometry and deformation quantization

Alena Pirutka  Varieties that are not stably rational, zerocycles and unramified cohomology

Takeshi Saito  On the proper pushforward of the characteristic cycle of a constructible sheaf

Tamás Szamuely and Gergely Zábrádi  The $p$adic Hodge decomposition according to Beilinson

Akio Tamagawa  Specialization of $\ell $adic representations of arithmetic fundamental groups and applications to arithmetic of abelian varieties

Olivier Wittenberg  Rational points and zerocycles on rationally connected varieties over number fields