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On the Arakelov Geometry of Moduli Spaces of Curves
Richard Hain, David Reed
In this paper we compute the asymptotics of the metric on the line bundle over the moduli space of curves that arises when attempting to compute the archimedean height of the algeb…
The rational cohomology ring of the moduli space of abelian 3-folds
Richard Hain
The rational cohomology ring of A_3, the moduli space of abelian 3-folds is computed. This is isomorphic to the the rational cohomology ring of the group Sp_3(Z) of 6x6 integral sy…
Iterated Integrals and Algebraic Cycles: Examples and Prospects
Richard Hain
This paper is for the proceedings of the Chen-Chow Conference held in Tianjin, China in October 2000. The goal of the paper is to produce and survey evidence for a connection betwe…
A De Rham-Witt approach to crystalline rational homotopy theory
Minhyong Kim, Richard M. Hain
We construct the crystalline fundamental group of a semi-stable variety over a field of positive characteristic using the log De Rham-Witt complex and Navarro-Aznar's derived Thom-…
Tannakian Fundamental Groups Associated to Galois Groups
Richard Hain, Makoto Matsumoto
This should be the final version of this paper. Numberous minor improvements have been made to the manuscript, one argument has been corrected, and an appendix has been added.
Weighted Completion of Galois Groups and Galois Actions on the Fundamental Group of P^1 - {0,1,infinity}
Richard Hain, Makoto Matsumoto
This is a revision of the paper that was previously entitled "Weighted Completion of Galois Groups and Some Conjectures of Deligne". Fix a prime number . We prove a conjecture s…