In contemporary a long time, $p$-adic geometry and $p$-adic cohomology theories became crucial instruments in quantity thought, algebraic geometry, and the idea of automorphic representations. The Arizona wintry weather tuition 2007, on which the present e-book relies, was once a different chance to introduce graduate scholars to this topic. Following worthy introductions by means of John Tate and Vladimir Berkovich, pioneers of non-archimedean geometry, Brian Conrad's bankruptcy introduces the overall conception of Tate's inflexible analytic areas, Raynaud's view of them because the familiar fibers of formal schemes, and Berkovich areas. Samit Dasgupta and Jeremy Teitelbaum talk about the $p$-adic higher part airplane for instance of a inflexible analytic house and provides functions to quantity concept (modular kinds and the $p$-adic Langlands program). Matthew Baker bargains a close dialogue of the Berkovich projective line and $p$-adic power concept on that and extra normal Berkovich curves. eventually, Kiran Kedlaya discusses theoretical and computational points of $p$-adic cohomology and the zeta features of types. This ebook should be a great addition to the library of any graduate pupil and researcher who's attracted to studying concerning the strategies of $p$-adic geometry.
Read Online or Download $p$-adic Geometry (University Lecture Series) PDF
Similar Algebraic Geometry books
This paintings attracts jointly principles from algebraic topology, practical research and geometry. it's a software - a method of conveying details between those 3 topics - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this publication is to acquaint the reader with the basic rules of analytic K-homology and strengthen a few of its functions.
First textbook-level account of uncomplicated examples and strategies during this zone. appropriate for self-study by way of a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yankee Mathematical Society, in addition to a winning Springer writer.
"It provides a delicate portrait of a superb person. It describes safely and intelligibly on a nontechnical point the area of mathematical rules during which Hilbert created his masterpieces. And it illuminates the heritage of German social historical past opposed to which the drama of Hilberts existence was once performed.
From the preface of the writer: ". .. i've got divided this paintings into books; within the first of those i've got constrained myself to these issues touching on natural research. within the moment e-book i've got defined these factor which has to be recognized from geometry, on account that research is regularly constructed in the sort of manner that its software to geometry is proven.
Additional info for $p$-adic Geometry (University Lecture Series)