Manual Projective Varieties and Modular Forms

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Projective Varieties and Modular Forms. Course Given at the University of Maryland, Spring Authors: Eichler, M. Free Preview.
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Course Given at the University of Maryland, Spring 1970

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Tsuyumine : On the Graded Rings of Modular Forms in Several Variables

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Boundedness results for singular Fano varieties (...) - Kebekus - Bourbaki - 19/01/19 - 3/4

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Given a curve C of genus bigger than one, it is open problem to find a practical method for determining the set of rational points of C.

Martin Eichler

In the Chabauty-Kim method, one approaches this problem by associating to a rational point a family of nonabelian Galois representations arising from the etale fundamental group of X at x, and instead trying to determine when such nonabelian Galois representations locally come from points on X. In this talk I will explain some recent developments in the theory. This is joint work with Jennifer Balakrishnan.

The notion of ordinary modular form is meaningless if the ordinary locus of the relevant Shimura variety is empty, so it seems impossible to generalize Hida theory to this situation. We can nevertheless replace the ordinary locus by the so called mu-ordinary locus introduced by Wedhorn, that is always not empty. In this talk we will explain how to generalize Hida theory over the mu-ordinary locus in some cases. Room F1. A classical result of Beauville shows that the action of the multiplication by n on the Chow ring of an abelian variety is semisimple with a finite number of explicit eigenvalues.

We might consider a bunch of equations, we might work over projective space, but let's keep it simple for now. The "almost all" is to avoid problems with bad primes. Thanks to Grothendieck, Deligne, and others, we have a very powerful bunch of tools for analysing this problem. The setup is as follows. So we get a slightly finer decomposition. It seems that this holds as long as one counts with respect to the appropriate "baseline". In this paper they give a class of examples.

Then, if I understand them correctly pg 7 , they say that if we set. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Modular forms from counting points on algebraic varieties over a finite field Ask Question.