ﻻ يوجد ملخص باللغة العربية
For a constructible etale sheaf on a smooth variety of positive characteristic ramified along an effective divisor, the largest slope in Abbes and Saitos ramification theory of the sheaf gives a divisor with rational coefficients called the conductor divisor. In this article, we prove decreasing properties of the conductor divisor after pull-backs. The main ingredient behind is the construction of etale sheaves with pure ramifications. As applications, we first prove a lower semi-continuity property for conductors of etale sheaves on relative curves in the equal characteristic case, which supplement Deligne and Laumons lower semi-continuity property of Swan conductors and is also an $ell$-adic analogue of Andres semi-continuity result of Poincare-Katz ranks for meromorphic connections on complex relative curves. Secondly, we give a ramification bound for the nearby cycle complex of an etale sheaf ramified along the special fiber of a regular scheme semi-stable over an equal characteristic henselian trait, which extends a main result in a joint work with Teyssier and answers a conjecture of Leal in a geometric situation.
Let X be a nonsingular projective algebraic variety, and let S be a line bundle on X. Let A = (a_1,..., a_n) be a vector of integers. Consider a map f from a pointed curve (C,x_1,...,x_n) to X satisfying the following condition: the line bundle f*(S)
Curves of genus g which admit a map to CP1 with specified ramification profile mu over 0 and nu over infinity define a double ramification cycle DR_g(mu,nu) on the moduli space of curves. The study of the restrictions of these cycles to the moduli of
We discuss two elementary constructions for covers with fixed ramification in positive characteristic. As an application, we compute the number of certain classes of covers between projective lines branched at 4 points and obtain information on the s
Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ of a discrete valuation ring $R$. Assume that the residue field $k$ of $R$ is perfect and that $mathop{textrm{char}} k eq 2$. Assume that the Weierstrass points of $C$ are $K$
Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ of a discrete valuation ring $R$. Assume that the residue field $k$ of $R$ is perfect and that $mathrm{char} k > 2g+1$. Let $S = mathrm{Spec} R$. Let $X$ be the minimal proper