{"product_id":"tale-cohomology-pms-33-volume-33-9780691171104","title":"Étale Cohomology (Pms-33), Volume 33","description":"\u003cp\u003eOne of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced  tale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and \u003ci\u003ep\u003c\/i\u003e-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to  tale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e The author begins with a review of the basic properties of flat and  tale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of  tale sheaves and elementary  tale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in  tale cohomology -- those of base change, purity, Poincar  duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series. \u003cp\u003e\u003c\/p\u003eOriginally published in 1980. \u003cp\u003e\u003c\/p\u003eThe \u003cb\u003ePrinceton Legacy Library\u003c\/b\u003e uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e James S. Milne\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 03\/21\/2017\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 344\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.04lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.70d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9780691171104\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eJ. S. Milne\u003c\/b\u003e is Professor Emeritus of Mathematics at the University of Michigan at Ann Arbor.\u003cbr\u003e\u003c\/p\u003e","brand":"Princeton University Press","offers":[{"title":"Paperback","offer_id":40384366084211,"sku":"9.78E+12","price":89.53,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/products\/img_517b5560-16d8-4771-b821-ca09949fac3c.jpg?v=1661435976","url":"https:\/\/bookstorenmore.com\/products\/tale-cohomology-pms-33-volume-33-9780691171104","provider":"Bookstore N More","version":"1.0","type":"link"}