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math.AG2002
New perspectives in Arakelov geometry
Caterina Consani, Matilde Marcolli
In this survey, written for the proceedings of the VII meeting of the CNTA held in May 2002 in Montreal, we describe how Connes' theory of spectral triples provides a unified view,…
math.AG2002
The Picard-Lefschetz formula and a conjecture of Kato, the case of Lefschetz fibrations
Caterina Consani, Minhyong Kim
A conjecture of Kato says that the monodromy operator on the cohomology of a semi-stable degeneration of projective varieties is represented by an algebraic cycle on the special fi…
math.AG2002
Non-commutative geometry, dynamics, and infinity-adic Arakelov geometry
Caterina Consani, Matilde Marcolli
In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the ``closed fibers at infinity''. Manin de…