Two meetings of the AMS in the fall of 1989--one at the Stevens Institute of Technology and the other at Ball State University--included Special Sessions on the role of \(p\)-adic methods in number theory and algebraic geometry. This volume grew out of these Special Sessions. Drawn from a wide area of mathematics, the articles presented here provide an excellent sampling of the broad range of trends and applications in \(p\)-adic methods.

Readership

Researchers and advanced graduate students working in number theory and algebraic geometry.

Table of Contents

• F. Baldassarri and B. Chiarellotto -- On Christol's theorem. A generalization to systems of PDE's with logarithmic singularities depending upon parameters
• F. Baldassarri and B. Chiarellotto -- On Andre's transfer theorem
• G. Christol and B. Dwork -- Differential modules of bounded spectral norm
• R. Crew -- The \(p\)-adic monodromy of a generic Abelian scheme in characteristic \(p\)
• D. R. Dorman -- Factorization of Drinfeld singular moduli
• B. Fisher -- Distinctness of Kloosterman sums
• R. M. Freije -- Intersection formulas for Mumford curves
• D. Goss -- \(L\)-series of Grössencharakters of type \(A_0\) for function fields
• G. Kato -- A \(p\)-adic cohomological method for the Weierstrass family and its zeta invariants
• M. Larsen -- Two-dimensional systems of Galois representations
• M. M. Robinson -- Algebraic identities useful in the computation of Igusa local zeta functions
• A. Silverberg -- Points of finite order on Abelian varieties
• P. F. Stiller -- The arithmetic and geometry of elliptic surfaces
• P. V. Mulbregt -- Torsion-points on low dimensional Abelian varieties with complex multiplication
• M. A. Vitulli -- Prime-like subsets of a commutative ring
• D. Wan -- Newton polygons and congruence decompositions of \(L\)-functions over finite fields