arXiv subjects

David Vauclair

Publications and source records attributed to David Vauclair.

4 recordsLinked to original sources

arXiv2017

On the non commutative Iwasawa main conjecture for abelian varieties over function fields

We establish the Iwasawa main conjecture for semi-stable abelian varieties over a function field of characteristic $p$ under certain restrictive assumptions. Namely we consider $p$-torsion free $p$-adic Lie extensions of the base field which contain the constant $\mathbb Z_p$-extension and are everywhere unramified. Under the classical $\mu=0$ hypothesis we give a proof which mainly relies on the interpretation of the Selmer complex in terms of $p$-adic cohomology [TV] together with the trace formulas of [EL1].

math.NT↗

arXiv2015

Logarithmic $p$-bases and arithmetical differential modules

We introduce the notion of log $p$-smoothness which weakens that of log-smoothness and that of having locally $p$-bases. We extend Berthelot's construction of arithmetic $D$-modules and some properties in this context.

math.AG↗

arXiv2015

A comparison theorem for semi-abelian schemes over a smooth curve

We compare flat cohomology with crystalline syntomic complexes in two cases: 1) $p$-divisible groups over a separated $\mathbb F_p$-scheme with local finite $p$-bases, 2) semi-abelian schemes over a separated irreducible smooth curve.

math.AG↗

arXiv2008

Sur la dualite et la descente d'Iwasawa

We develop a formalism for studying descent and codescent in the context of Iwasawa theory. The main result essentially states that to control descent or codescent amounts to the same. Arithmetic applications are given.

math.NT↗