By Asher Auel,Brendan Hassett,Anthony Várilly-Alvarado,Bianca Viray

The contributions during this booklet discover a number of contexts within which the derived type of coherent sheaves on a range determines a few of its mathematics. This environment presents new geometric instruments for analyzing components of the Brauer staff. With a view in the direction of destiny mathematics functions, the booklet extends a couple of robust instruments for reading rational issues on elliptic curves, e.g., isogenies between curves, torsion issues, modular curves, and the ensuing descent strategies, in addition to higher-dimensional types like K3 surfaces. encouraged through the fast fresh advances in our figuring out of K3 surfaces, the booklet is meant to foster cross-pollination among the fields of advanced algebraic geometry and quantity theory.

Contributors:

· Nicolas Addington

· Benjamin Antieau

· Kenneth Ascher

· Asher Auel

· Fedor Bogomolov

· Jean-Louis Colliot-Thélène

· Krishna Dasaratha

· Brendan Hassett

· Colin Ingalls

· Martí Lahoz

· Emanuele Macrì

· Kelly McKinnie

· Andrew Obus

· Ekin Ozman

· Raman Parimala

· Alexander Perry

· Alena Pirutka

· Justin Sawon

· Alexei N. Skorobogatov

· Paolo Stellari

· Sho Tanimoto

· Hugh Thomas

· Yuri Tschinkel

· Anthony Várilly-Alvarado

· Bianca Viray

· Rong Zhou

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