The first identification is very general it is true for any cohomology theory on a. In this paper, we study the indecomposability which is also a grouptheoretic property of profinite groups of various anabelian profinite groups. Etale cohomology tom sutherland october, 2008 note. Lei fu etale cohomology is an important branch in arithmetic geometry. Our approach uses the ramification theory of abbes and saito, and relies on tsushimas refined characteristic class. I large enough so that all the coefficients of the fjs lie in bi, and. Fu, etale cohomology theory, revised edition, world scientific, 2015. 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. Along the way, we establish various foundational results on the geometry of the hodgetate period map. A structure theory for prolie algebras, prolie groups, and connected locally compact groups european mathematical society karl h. Lei fu, etale cohomology theory is also nice and has not been mentioned yet.
Etale cohomology of schemes and analytic spaces article pdf available in lecture notes in mathematics springerverlag 2119 january 2011 with 84 reads how we measure reads. After a very brief discussion of functoriality, this construction immediately implies. Lei fu etale cohomology theory revised edition revised. Introduction to lie algebra cohomology with a view towards. In the presented homology and cohomology solver, the extraction of the cell complex from the. Pdf etale cohomology theory download ebook for free. Sheaf theory etale cohomology is modelled on the cohomology theory of sheaves in the. Click download or read online button to etale cohomology theory book pdf for free now. Etale cohomology theoryrevised editio nankai tracts in mathematics book 14 kindle edition by lei fu. Sheaf theory etale cohomology is modelled on the cohomology theory of.
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. In this article, assuming the universal local acyclicity, we show an analogous result of the continuity of. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of af. Etale cohomology theory by lei fu overdrive rakuten. Etale cohomology theoryrevised editio and millions of other books are available for amazon kindle. This is a very short overview on lie algebra cohomology. Etale cohomology theory nankai tracts in mathematics by lei fu. 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. Download etale cohomology is an important branch in arithmetic geometry. The goal of this paper is to show that the cohomology of compact unitary shimura varieties is concentrated in the middle degree and torsion free, after localizing at a maximal ideal of the hecke algebra satisfying a suitable genericity assumption. The etale cohomology with coefficients in the constant etale sheaf q. To a digraph with a choice of certain integral basis, we construct a cw complex, whose integral singular cohomology is canonically isomorphic to the path cohomology of the digraph as introduced in \\citeglmy.
Etheory is the universal localization calg e \to e which is homotopyinvariant, stable and preserves exact sequences in the middle relation to kktheory. Use features like bookmarks, note taking and highlighting while reading etale cohomology theoryrevised editio nankai tracts in mathematics book 14. Algebraic ltheory, also known as hermitian ktheory, is important in surgery theory. C2,c1,c0 are the free abelian groups generated by the set of faces. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Etale cohomology is an important branch in arithmetic geometry. Refined characteristic class and conductor formula. Pdf etale cohomology of schemes and analytic spaces. For example, the first cohomology group of a complex elliptic curve is a free module of rank 2 over the integers.
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex. The objects of this category are etale morphisms see cohomology in algebraic geometry of schemes to, while the morphisms are etale morphisms such that if is another etale morphism to, then. The key to the proof of our results is the consideration of the homology theory e, oz mu. Given a presheaf of sets g, we define the free abelian presheaf on g, denoted zg.
More generally, there is etale generalized cohomology theory with coefficients in sheaves of spectra on the etale site jardine 97. Etale cohomology theory nankai tracts in mathematics. In this article, we prove a conductor formula in a geometric situation which is an analogue of the grothendieckoggshafarevich formula. A field theory for leading from the emerging future fehler. 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. Contemporary trends in algebraic geometry and algebraic topology. This shows that every point is open, so that y carries the discrete. Additional gift options are available when buying one ebook at a time. Homology and cohomology computation in fe modeling 3 usual input for homology or cohomology computation. Evan jenkinss notes of a seminar on etale cohomology click on the pdf icons. Fu, etale cohomology theory, revised edition, world scienti. In mathematics, algebraic ltheory is the ktheory of quadratic forms. The topological questions on compact lie groups, once they have been reduced to algebraic questions on lie algebras, suggest a certain number of purely algebraic objects, which may be constructed in relation with any lie. In general we expect that the cohomology theory at step n is a twist between the cohomology from step n 1 with an appropriate cohomology theory that depends only.
These notes are an introduction to the theory of algebraic varieties emphasizing the similarities to the theory of manifolds. Valentina di proietto seminar on dmodules elena lavanda and wouter zomervrucht two students seminars on algebraic groups lei zhang and riemann surfaces valentina di proietto. Grothendiecks approach for the etale cohomology and since then for many other theories. Craig westerland, a higher chromatic analogue of the image of j arxiv. This approach leads more naturally into scheme theory. 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. 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. Use this tag for questions about a particular construction of homological algebra of an abelian category a that refines and in a certain sense simplifies the theory of derived functors defined on a. Dwyer and friedlander interpreted important arithmetic questions in terms of this galois action on etale ktheory. Lectures on etale cohomology harvard mathematics department. Some versions of cohomology arise by dualizing the construction of homology.
In page 3 of lei fus etale cohomology theory, there is a notion called discrete valuation ring as follows. 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. Newest etalecohomology questions mathematics stack. On the generic part of the cohomology of compact unitary. We want to first define the category see category theory called or in the literature. Topologists would use these data in order to analyze the manifold by means of morse theory, that is by studying the dynamical system. Etale cohomology pro and con todays lecture has a somewhat schizophrenic goal. Many recent applications of physics to topology are based on. But about discrete valuation, i have found two different definitions. Classically, it is wellknown that various anabelian profinite groups, i.
Newest derivedcategories questions mathematics stack. Lei fu etale cohomology theory revised edition revised edition. A tutorial on quantum cohomology alexander givental uc berkeley let m,f,g be a manifold, a function and a riemann metric on the manifold. Cohomology theory article about cohomology theory by the. Extension of modules in this section, we describe basics of the theory of module extension functors, and we relate it to group cohomology in the following section. A very nice feature of fus work is the inclusion of some relevant.
Because kktheory is the universal split exact stable and homotopyinvariant localization of calg, and etheory the universal halfexact localization, and since every split exact sequence is. By author lei fu chern institute of mathematics, nankai university, china. This book covers the main materials in sga 1, sga 4, sga 4 12 and sga 5 on etale c mathematics nonfiction. This chapter summarizes the theory of the etale topology on schemes, culmi. New edition available here etale cohomology is an important branch in arithmetic geometry. Etale cohomology theory by lei fu, 9789814307727, available at book depository with free delivery worldwide. Hisham sati, craig westerland, twisted morava ktheory and etheory arxiv. 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. From now on e shall always denote a landweber exact cohomology theory with representing gspectrum e, which satisfies the hypotheses outlined in the statement of theorem 2. Linear algebraic groups s if q c, every affine algebraic group g can be viewed as a complex lie group. Etale cohomology theoryrevised editio nankai tracts in. The homotopy type of the cw complex turns out to be independent of the choice of basis.
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