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Equazioni differenziali p -adiche e interpolazione p -adica di formule classiche

Francesco Baldassarri (2000)

Bollettino dell'Unione Matematica Italiana

We shortly introduce non-archimedean valued fields and discuss the difficulties in the corresponding theory of analytic functions. We motivate the need of p -adic cohomology with the Weil Conjectures. We review the two most popular approaches to p -adic analytic varieties, namely rigid and Berkovich analytic geometries. We discuss the action of Frobenius in rigid cohomology as similar to the classical action of covering transformations. When rigid cohomology is parametrized by twisting characters,...

Equivalence of families of singular schemes on threefolds and on ruled fourfolds.

Flaminio Flamini (2004)

Collectanea Mathematica

The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for families of...

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