ec 2 00 7 Character sums to smooth moduli are small

D ec 2 00 7 Character sums to smooth moduli are small

(where χ (mod q) is a Dirichlet character) arise naturally in many classical problems of analytic number theory, from estimating the least quadratic nonresidue (mod p) to bounding L-functions. Recall that for any character χ (mod q) , |Sχ(x)| is trivially bounded above by φ(q). A folklore conjecture (which is a consequence of the Generalized Riemann Hypothesis) predicts that for nonprincipal ch...

M ar 2 00 8 Smooth models of quiver moduli

For any moduli space of stable representations of quivers, certain smooth varieties, compactifying projective space fibrations over the moduli space, are constructed. The boundary of this compactification is analyzed. Explicit formulas for the Betti numbers of the smooth models are derived. In the case of moduli of simple representations, explicit cell decompositions of the smooth models are co...

un 2 00 7 Profinite complexes of curves , their automorphisms and anabelian properties of moduli stacks of curves

Let M g,[n] , for 2g − 2 + n > 0, be the Deligne-Mumford (briefly D-M) moduli stack of smooth curves of genus g labeled by n unordered distinct points. The main result of the paper is that a finite, connectedétale cover M λ of M g,[n] , defined over a sub-p-adic field k, is " almost " anabelian in the sense conjectured by Grothendieck for curves and their moduli spaces.

ar X iv : a st ro - p h / 05 12 61 7 v 1 2 7 D ec 2 00 5 3 D Spectroscopy of Herbig - Haro objects

1 M ay 2 00 7 BOUNDS ON EXPONENTIAL SUMS OVER SMALL MULTIPLICATIVE SUBGROUPS PÄR

We show that there is significant cancellation in certain exponential sums over small multiplicative subgroups of finite fields, giving an exposition of the arguments by Bourgain and Chang [6].