arXiv subjects

Xavier Xarles

Publications and source records attributed to Xavier Xarles.

20 records · Page 2Linked to original sources

arXiv2006

On the etale cohomology of algebraic varieties with totally degenerate reduction over p-adic fields

Let K be a finite extension of Q_p and X a smooth projective variety over K. We define the notion of totally degenerate reduction of such an X and the associated Chow complexes of the special fibre of a suitable regular proper model of X over the ring of integers of K. If X has such reduction, we then show that for all l, the Q_l-adic etale cohomology of X has a filtration whose graded quotients are isomorphic, as Galois modules, to the tensor product of a finite dimensional Q-vector space (with a finite unramified action of Galois) with twists of Q_l by the cyclotomic character.

math.AG↗

arXiv2006

On p-adic intermediate Jacobians

For an algebraic variety $X$ of dimension $d$ with totally degenerate reduction over a $p$-adic field (definition recalled below) and an integer $i$ with $1\leq i\leq d$, we define a rigid analytic torus $J^i(X)$ together with an Abel-Jacobi mapping to it from the Chow group $CH^i(X)_{hom}$ of codimension $i$ algebraic cycles that are homologically equivalent to zero modulo rational equivalence. These tori are analogous to those defined by Griffiths using Hodge theory over the complex numbers. We compare and contrast the complex and $p$-adic theories. Finally, we examine a special case of a $p$-adic analogue of the Generalized Hodge Conjecture

math.NT↗