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This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of thep-adic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey articles

Geometry, Algebraic. --- Number theory. --- p-adic analysis. --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Number study --- Numbers, Theory of --- Algebraic geometry --- Geometry