Lei fu etale cohomology theory pdf files

Fundamental group and etale cohomology mathoverflow. This note and course is based especially on mil80, mil, har77, fk88, jan15, lev. Etale cohomology theoryrevised editio nankai tracts in mathematics book 14 kindle edition by lei fu. Etale cohomology theory nankai tracts in mathematics.

Lei fu, etale cohomology theory is also nice and has not been. Etale cohomology theory mathematical association of america. This is a course note for etale cohomology fu, 2018. A very nice feature of fus work is the inclusion of some relevant. We show that the cohomology of gsp is often isomorphic to the etale cohomology of the scheme specok \ s. Lei fu, etale cohomology theory is also nice and has not been mentioned yet. Sheaf theory etale cohomology is modelled on the cohomology theory of sheaves in the usual topological sense. Serre, that illuminates some of the difficulties in constructing a weil cohomology. Etale cohomology theory nankai tracts in mathematics nankai tracts in mathematics hardcover 9789814307727. Much of the material in these notes parallels that in, for example, iversen, b. 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 sheaves of spectra on the etale site jardine 97. Fu, algebraic geometry, tsinghua university press and springer.

Fu, etale cohomology theory, revised edition, world scientific, 2015. Etale cohomology etale cohomology theory world scientific. Isbn 9780387121758 fu, lei 2011, etale cohomology theory. Lic2009b, and the conjectural underlying cohomology theory is known. 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. Contemporary trends in algebraic geometry and algebraic topology. Zetavalues of arithmetic schemes at negative integers and weil. 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. Evan jenkinss notes of a seminar on etale cohomology click on the pdf icons. Etale cohomology is an important branch in arithmetic geometry. Etale cohomology theoryrevised editio nankai tracts in. The essentials of etale cohomology theory springerlink. The essentials of etale cohomology theory springerlink skip. These are the notes for a course taught at the university of michigan in w89 as math 732and in w98 as math 776.