Ambrus Pál

The real section conjecture and Smith's fixed-point theorem for pro-spaces

We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes equipped with the action of a group of prime order

Solvable Points on Projective Algebraic Curves

p

On the Kernel and the Image of the Rigid Analytic Regulator in Positive Characteristic

whose

ON THE EISENSTEIN IDEAL OF DRINFELD MODULAR CURVES

p

Rigid cohomology over Laurent series fields

-torsion cohomology can be killed by finite covers. As an application we derive the section conjecture for the real points of a large class of varieties defined over the field of real numbers and the natural analogue of the section conjecture for fixed points of finite group actions on projective curves of positive genus defined over the field of complex numbers.

A Rigid Analytical Regulator for the K2 of Mumford Curves

We examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g, when g is at least 40, over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 defined over any field has a solvable point. Finally we prove that every genus 1 curve defined over a local field of characteristic zero with residue field of characteristic p has a divisor of degree prime to 6p defined over a solvable extension. Received by the editors August 27, 2002. AMS subject classification: 14H25,11D88. c ©Canadian Mathematical Society 2004. 612

The Rigid Analytical Regulator and K2 of Drinfeld Modular Curves

We will formulate and prove a certain reciprocity law relating certain residues of the differential symbol dlog2 from the K2 of a Mumford curve to the rigid analytic regulator constructed by the author in a previous paper. We will use this result to deduce some consequences on the kernel and image of the rigid analytic regulator analogous to some old conjectures of Beilinson and Bloch on the complex analytic regulator. We also relate our construction to the symbol defined by ContouCarrere and to Kato’s residue homomorphism, and we show that Weil’s reciprocity law directly implies the reciprocity law of Anderson and Romo.

Theta Series, Eisenstein Series and Poincare Series over Function Fields

Let

Finiteness with Coefficients via a Local Monodromy Theorem

\goth E(\goth p)

The Overconvergent Site, Descent, and Cohomology with Compact Support

denote the Eisenstein ideal in the Hecke algebra