The local monodromy as a generalized algebraic correspondence

1998/01/17 by Caterina Consani, Consani, Caterina
Mathematics · #14C25 #14C30 #14D07 #14E10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C25 #msc:14C30 #msc:14D07 #msc:14E10

paper · pdf · doi:10.48550/arxiv.math/9801080

41 pages, LaTeX2e

arxiv created 1998/01/17 · arxiv updated 2009/11/30

Abstract

In the paper we show that for a normal-crossings degeneration Z over the ring of integers of a local field with X as generic fibre, the local monodromy operator and its powers determine invariant cocycle classes under the decomposition group in the cohomology of the product X × X. More precisely, they also define algebraic cycles on the special fibre of a resolution of Z × Z. In the paper, we give an explicit description of these cycles for a degeneration with at worst triple points as singularities. These cycles explain geometrically the presence of poles on specific local factors of the L-function related to X × X.

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