02487nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084003600184100003300220245009500253260008200348300003400430336002600464337002600490338003600516347002400552490005300576506006500629520110700694650002601801650002301827650005501850650004001905650002801945700002901973856003202002856006702034227-180108CH-001817-320180108234002.0a fot ||| 0|cr nn mmmmamaa180108e20180122sz fot ||| 0|eng d a978303719635970a10.4171/1352doi ach0018173 7aPBR2bicssc a11-xxa06-xxa13-xxa14-xx2msc1 aFujiwara, Kazuhiro,eauthor.10aFoundations of Rigid Geometry Ih[electronic resource] /cKazuhiro Fujiwara, Fumiharu Kato3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (863 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttp://www.ems-ph.org/ebooks.php aRigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate’s rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean
valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich structures, based on discoveries of its relationship with birational and formal geometries.
In this research monograph, foundational aspects of rigid geometry are discussed, putting emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion on the relationship with Tate‘s original rigid analytic geometry,
V.G. Berkovich‘s analytic geometry and R. Huber‘s adic spaces. As a model example of applications, a proof of Nagata‘s compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost
self-contained.07aNumber theory2bicssc07aNumber theory2msc07aOrder, lattices, ordered algebraic structures2msc07aCommutative rings and algebras2msc07aAlgebraic geometry2msc1 aKato, Fumiharu,eauthor.40uhttps://doi.org/10.4171/135423cover imageuhttp://www.ems-ph.org/img/books/fujiwara_mini.jpg