Chern Numbers of Algebraic Surfaces.
Chern numbers of cusp resolutions in totally real cubic number fields.
Chern numbers of Hilbert modular varieties.
Class 2 Galois representations of Kummer type.
Class invariants by Shimura's reciprocity law
We apply the Shimura reciprocity law to determine when values of modular functions of higher level can be used to generate the Hilbert class field of an imaginary quadratic field. In addition, we show how to find the corresponding polynomial in these cases. This yields a proof for conjectural formulas of Morain and Zagier concerning such polynomials.
Class numbers, Jacobi forms and Siegel-Eisenstein series of weight 2 on Sp2.
Classes d'idéaux et classes de diviseurs
Classical and overconvergent modular forms
Classical and overconvergent modular forms of higher level
We define the notion overconvergent modular forms on where is a prime, and are positive integers and is prime to . We show that an overconvergent eigenform on of weight whose -eigenvalue has valuation strictly less than is classical.
Classical projective geometry and arithmetic groups.
Closed geodesics, periods and arithmetic of modular forms.
CM points and quaternion algebras.
Cocycles d'Euler et de Maslov.
Coefficient bounds for level 2 cusp forms
We give explicit upper bounds for the coefficients of arbitrary weight k, level 2 cusp forms, making Deligne’s well-known bound precise. We also derive asymptotic formulas and explicit upper bounds for the coefficients of certain level 2 modular functions.
Co-fibered products of algebraic curves
We give examples of failure of the existence of co-fibered products in the category of algebraic curves.
Cohen-Kuznetsov liftings of quasimodular forms
Jacobi-like forms for a discrete subgroup Γ of SL(2,ℝ) are formal power series which generalize Jacobi forms, and they correspond to certain sequences of modular forms for Γ. Given a modular form f, a Jacobi-like form can be constructed by using constant multiples of derivatives of f as coefficients, which is known as the Cohen-Kuznetsov lifting of f. We extend Cohen-Kuznetsov liftings to quasimodular forms by determining an explicit formula for a Jacobi-like form associated to a quasimodular form....
Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems
The aim of these notes is to generalize Laumon’s construction [20] of automorphic sheaves corresponding to local systems on a smooth, projective curve to the case of local systems with indecomposable unipotent ramification at a finite set of points. To this end we need an extension of the notion of parabolic structure on vector bundles to coherent sheaves. Once we have defined this, a lot of arguments from the article “ On the geometric Langlands conjecture” by Frenkel, Gaitsgory and Vilonen [11]...
Cohomologie des espaces de formes automorphes
Cohomologie d’intersection et fonctions de certaines variétés de Shimura
Cohomologie, -groupes et fonctorialité