Topics in Ramification Theory

摘要

This thesis treats several topics in ramification theory. Let K be a complete discrete valuation field whose residue field is perfect and of positive characteristic.;The first topic treated is ramification of etale cohomology. More precisely, let X be a connected, proper scheme over OK , and U be the complement in X of a divisor with simple normal crossings. Assume that the pair ( X,U) is strictly semi-stable over OK of relative dimension one and K is of equal characteristic. We prove that, for any smooth l-adic sheaf G on U of rank one, at most tamely ramified on the generic fiber, if the ramification of G is bounded by t+ for the logarithmic upper ramification groups of Abbes-Saito at points of codimension one of X, then the ramification of the etale cohomology groups with compact support of G is bounded by t+ in the same sense.;The second topic treated is ramification in transcendental extensions of local fields. Let L/K be a separable extension of complete discrete valuation fields. The residue field of L is not assumed to be perfect. We prove a formula for the Swan conductor of the image of a sufficiently ramified character from H1( K, Q/Z) in H1(L, Q/Z).;Finally, we treat generalized Hasse-Herbrand functions. We define generalizations of the classical Hasse-Herbrand function and study their properties.