A fixed point formula for varieties over finite fields.
A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula
This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.
A formula for the Cartier operator on plane algebraic curves.
A Gauss-Bonnet theorem for motivic cohomology.
A generalization of formal schemes and rigid analytic varieties.
A Higher Dimensional Analogue of Mordell's Conjecture Over Function Fields.
A moduli approach to quadratic -curves realizing projective mod Galois representations.
A motivic Chebotarev density theorem.
A new construction of -adic -functions attached to certain elliptic curves with complex multiplication
In this paper we apply the results of our previous article on the -adic interpolation of logarithmic derivatives of formal groups to the construction of -adic -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.
A new cubic character sum
A new record for the canonical height on an elliptic curve over .
A note on elliptic curves over finite fields
A note on Enriques' surfaces in characteristic 2
A note on functional equations for zeta functions with values in Chow motives
We consider zeta functions with values in the Grothendieck ring of Chow motives. Investigating the –structure of this ring, we deduce a functional equation for the zeta function of abelian varieties. Furthermore, we show that the property of having a rational zeta function satisfying a functional equation is preserved under products.
A Note on height pairings on polarized abelian varieties
Let be an abelian variety defined over a number field . In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.
A Note on Height Pairings, Tamagawa Numbers, and the Birch and Swinnerton-Dyer Conjecture.
A Note on the First Rigid Cohomology Group for Geometrically Unibranch Varieties
A note on the Hasse principle
A -adic regulator map and finiteness results for arithmetic schemes.
A procedure to calcute torsion of elliptic curves over Q.