System upgrade on feb 12th during this period, ecommerce and registration of new users may not be available for up to 12 hours. Grothendieck was the rst to suggest etale cohomology 1960 as an attempt to solve the weil conjectures. In this article, we prove a conductor formula in a geometric situation which is an analogue of the grothendieckoggshafarevich formula. Poincare duality for etale cohomology tony feng february 1, 2017 contents 1 statementofpoincareduality 1 2 thetracemap 3 3 derivedcategories 10 4 thedualitytheorem 16. Essentials of integration theory for analysis daniel w. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of af. Galois cohomology is the derived functor see more on chain complexes and the hom and tensor functors of. All schemes are taken to be noetherian and separated 1 introduction the development of etale cohomology was motivated by work on the weil conjectures, which state that localzeta functions x. Galois cohomology is the derived functor see more on chain complexes and the hom and tensor functors of the fixed module functor. In mathematics, the etale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by grothendieck in order to prove the weil conjectures.
Our approach uses the ramification theory of abbes and saito, and relies on tsushimas refined characteristic class. Algebraic geometry i shall assume familiarity with the theory of algebraic varieties, for. In this article, assuming the universal local acyclicity, we show an analogous result of the continuity of. Fu, algebraic geometry, tsinghua university press and springer. Use features like bookmarks, note taking and highlighting while reading etale cohomology theoryrevised editio nankai tracts in mathematics book 14. Etale cohomology theory download ebook pdf, epub, tuebl. World scientific publishing company february 28, 2011 isbn. Download it once and read it on your kindle device, pc, phones or tablets. Nigel higson, categories of fractions and excision in kktheory j. Use for questions related to descent theory in topology. Lei fu, etale cohomology theory is also nice and has not been.
For a locally constant sheaf on the complement of a divisor in x flat over s, deligne and laumon proved that the universal local acyclicity is equivalent to the local constancy of swan conductors. Refined characteristic class and conductor formula springerlink. Introduction to kktheory and etheory, lecture notes lisbon 2009 a standard textbook account is in section 25 of. Download etale cohomology is an important branch in arithmetic geometry. The first identification is very general it is true for any cohomology theory on a site and has nothing to do with the. These notes are an introduction to the theory of algebraic varieties emphasizing the similarities to the theory of manifolds. Sheaf theory etale cohomology is modelled on the cohomology theory of sheaves in the usual topological sense. Lei fu etale cohomology is an important branch in arithmetic geometry. Evan jenkinss notes of a seminar on etale cohomology click on the pdf icons. Etale cohomology is an important branch in arithmetic geometry.
Pdf etale cohomology theory download ebook for free. New edition available here etale cohomology is an important branch in arithmetic geometry. Algebraic ltheory, also known as hermitian ktheory, is important in surgery theory. Grothendieck topologies and etale cohomology pieter belmans. This book covers the main materials in sga 1, sga 4, sga 4 12 and sga 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ladic cohomology. Etale cohomology theory nankai tracts in mathematics lei fu hardcover. The sheaf cohomology will be replaced by the derived category of a ringed topos. Evan jenkinss notes of a seminar on etale cohomology click on the pdf. Algebraic geometry i shall assume familiarity with. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Or alternatively, lei fu s etale cohomology book, which essentially is a dryer and more detailed version of the relevant egasin english i might add. The weiletale topology for number rings annals of mathematics.
Much of the material in these notes parallels that in, for example, iversen, b. Because such results are still coming in, and raise many possibilities, comprehensive treatments of etale cohomology even through lei fu, etale cohomology theory nankai tracts in mathematics are still substantially based on the sga, including sga 4. Antoine ducros, etale cohomology of schemes and analytic spaces, pdf. Note that, however, the category of chow motives does not give a weil cohomology theory since it is not abelian. Tammes book on etale cohomology this is a detailed exposition of artins book. Etale cohomology tom sutherland october, 2008 note. The latter property makes it in general computable.
Newest descent questions mathematics stack exchange. For instance, we prove that the etale fundamental group of the configuration space of a. Etale cohomology theoryrevised editio nankai tracts in. Weil cohomology theories play an important role in the theory of motives, insofar as the category of chow motives is universal for weil cohomology theories in the sense that any weil cohomology theory factors through chow motives.
Etale cohomology theoryrevised editio nankai tracts in mathematics book 14 kindle edition by lei fu. In mathematics, algebraic ltheory is the ktheory of quadratic forms. By author lei fu chern institute of mathematics, nankai university, china. Download pdf etalecohomologytheory free online new. This book covers the main materials in sga 1, sga 4, sga 4 12 and sga 5 on etale cohomology theory, which includes decent theory, etale fundamental groups.
Bilinear forms with kloosterman sums and applications. We prove nontrivial bounds for general bilinear forms in hyperkloosterman sums when the sizes of both variables may be below the range controlled by. Lei fu, etale cohomology theory, nankai tracts in math. Etale cohomology theory nankai tracts in mathematics by lei fu. If youre looking for all the basics definitions, background, first results id suggest you look at ega iv. Lam on his 70th birthday, 31st ohio statedenison mathematics conference, may.
Or alternatively, lei fus etale cohomology book, which essentially is a dryer and more detailed version of the relevant egasin english i might add. This approach leads more naturally into scheme theory. Etale cohomology etale cohomology theory world scientific. Etale cohomology lei zhang february 8, 2017 introduction in this course we are going to follow closely sga1 and sga4 to develop an abstract framwork of fundamental groups and cohomology theory.
Etale cohomology theory nankai tracts in mathematics. One of the main reasons that it fails to give the results that we would want is that if xis a complex variety and fis a constant sheaf then hi zarx. Linear algebraic groups s if q c, every affine algebraic group g can be viewed as a complex lie group. Click download or read online button to etale cohomology theory book pdf for free now. Lei fu, etale cohomology theory is also nice and has not been mentioned yet. Etale cohomology is an important branch in arithmetic. Classically, it is wellknown that various anabelian profinite groups, i. Download limit exceeded you have exceeded your daily download allowance. The moduli space of cubic threefolds as a ball quotient memoirs of the american mathematical society daniel allcock, james a. Etale cohomology theory by lei fu overdrive rakuten. Fu, etale cohomology theory, revised edition, world scientific, 2015. Proetale cohomology helene esnault, lars kindler, lei zhang march 17, 2014 introduction the etale cohomology theory which was initially suggested by grothendieck in 1960s plays a very important role in modern algebraic geometry. This book covers the main materials in sga 1, sga 4, sga 4 12 and sga 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, galois cohomology, etale cohomology, derived categories, base change theorems, duality, and.
More generally, there is etale generalized cohomology theory with coefficients in. In this paper, we study the indecomposability which is also a grouptheoretic property of profinite groups of various anabelian profinite groups. A structure theory for prolie algebras, prolie groups, and connected locally compact groups. This book covers the main materials in sga 1, sga 4, sga 4 12 and sga 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, galois cohomology, etale cohomology, derived categories, base change theorems, duality. More generally, there is a connection between the etale cohomology of a field and galois cohomology, an important part of algebraic number theory that we now define. Fq f be the base change of x 0, let l 0 be a lisse q.
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