Related papers: On integral images of Curtis homomorphisms for $\m…

We study the endomorphism algebras of a modular Gelfand-Graev representation of a finite reductive group by investigating modular properties of homomorphisms constructed by Curtis and Curtis-Shoji.

In this note we give explicit computations of certain types of Curtis homomorphisms and interpret them in terms of Gelfand-Tsetlin diagrams. Namely, this interpretation follows from Gelfand-Tsetlin formulas for the…

After recent work of Hill, Hopkins, and Ravenel on the Kervaire invariant one problem, as well as Adams' solution of the Hopf invariant one problem, an immediate consequence of Curtis conjecture is that the set of spherical classes in…

For a coarse space $(X, \mathcal{E})$, $X^\sharp$ denotes the set of all unbounded ultrafilters on $X$ endowed with the parallelity relation: $p||q$ if there exists $E \in \mathcal{E} $ such that $ E[P]\in q $ for each $P\in p$. If $(X,…

Let k be an algebraically closed field of characteristic p. Let X(p^e;N) be the curve parameterizing elliptic curves with full level N structure (where p does not divide N) and full level p^e Igusa structure. By modular curve, we mean a…

A curve X over the field Q of rational numbers is modular if it is dominated by X_1(N) for some N; if in addition the image of its jacobian in J_1(N) is contained in the new subvariety of J_1(N), then X is called a new modular curve. We…

The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of…

We show that central extensions of the mapping class group $M_g$ of the closed orientable surface of genus $g$ by $\Z$ are residually finite. Further we give rough estimates of the largest $N=N_g$ such that homomorphisms from $M_g$ to SU(N)…

This is a survey on recent results on counting of curves over finite fields. It reviews various results on the maximum number of points on a curve of genus g over a finite field of cardinality q, but the main emphasis is on results on the…

Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\mathcal{C}(N)$ be the curve complex of $N$. We prove that if $(g, n) \neq (1,2)$ and $g + n \neq 4$, then there is an exhaustion of…

We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…

Let $\mathcal{X}$ be an irreducible algebraic curve defined over a finite field $\mathbb{F}_q$ of characteristic $p>2$. Assume that the $\mathbb{F}_q$-automorphism group of $\mathcal{X}$ admits as an automorphism group the direct product of…

We produce a sequence of finite dimensional representations of the fundamental group $\pi_1(S)$ of a closed surface where all simple closed curves act with finite order, but where each non--simple closed curve eventually acts with infinite…

Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…

For a group $G$ and $R=\mathbb Z,\mathbb Z/p,\mathbb Q$ we denote by $\hat G_R$ the $R$-completion of $G.$ We study the map $H_n(G,K)\to H_n(\hat G_R,K),$ where $(R,K)=(\mathbb Z,\mathbb Z/p),(\mathbb Z/p,\mathbb Z/p),(\mathbb Q,\mathbb…

Let F be a totally real number field, n a prime integer, and G a unitary group of rank n defined over F that is compact at every infinite place. We prove an asymptotic formula for the number of cuspidal automorphic representations of G…

Let $f: X \to Y$ be a regular covering of a surface $Y$ of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group $G$. We give necessary and sufficient conditions for an integral homology class on $X$ to…

In this paper we give an explicit description of the universal unitary completion of certain locally Q_p-analytic representations of GL_2(F), where F is a finite extension of Q_p (this generalizes some results of Berger-Breuil for F=Q_p).…

Let G be a reductive group over an algebraically closed field of characteristic p, and let u in G be a unipotent element of order p. Suppose that p is a good prime for G. We show in this paper that there is a homomorphism phi:SL_2/k --> G…

We describe an algorithm to compute the number of points over finite fields on a broad class of modular curves: we consider quotients $X_H/W$ for $H$ a subgroup of $\GL_2(\mathbb Z/n\mathbb Z)$ such that for each prime $p$ dividing $n$, the…