Link Download ebook Free: https://ouo.io/PLxmr0l Geometry Over Nonclosed Fields By: Fedor Bogomolov Publisher: Springer Print ISBN: 9783319497624, 3319497626 eText ISBN: 9783319497631, 3319497634 Copyright year: 2017 Format: PDF Available from $ 169.00 USD SKU 9783319497631 Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.
