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Covers in p -adic analytic geometry and log covers I: Cospecialization of the ( p ) -tempered fundamental group for a family of curves

Emmanuel Lepage (2013)

Annales de l’institut Fourier

The tempered fundamental group of a p -adic analytic space classifies covers that are dominated by a topological cover (for the Berkovich topology) of a finite étale cover of the space. Here we construct cospecialization homomorphisms between ( p ) versions of the tempered fundamental groups of the fibers of a smooth family of curves with semistable reduction. To do so, we will translate our problem in terms of cospecialization morphisms of fundamental groups of the log fibers of the log reduction and...

Cubic surfaces with a Galois invariant double-six

Andreas-Stephan Elsenhans, Jörg Jahnel (2010)

Open Mathematics

We present a method to construct non-singular cubic surfaces over ℚ with a Galois invariant double-six. We start with cubic surfaces in the hexahedral form of L. Cremona and Th. Reye. For these, we develop an explicit version of Galois descent.

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