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See detailOn Galois Representations of Weight One
Wiese, Gabor UL

in Documenta Mathematica (2014), 19

A two-dimensional Galois representation into the Hecke algebra of Katz modular forms of weight one over a finite field of characteristic p is constructed and is shown to be unramified at p in most cases.

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See detailQuillen homology for operads via Gröbner bases
Dotsenko, Vladimir UL; Khoroshkin, Anton

in Documenta Mathematica (2013), 18

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See detailDihedral Galois representations and Katz modular forms
Wiese, Gabor UL

in Documenta Mathematica (2004), 9

We show that any two-dimensional odd dihedral representation \rho over a finite field of characteristic p>0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of ... [more ▼]

We show that any two-dimensional odd dihedral representation \rho over a finite field of characteristic p>0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N, character \epsilon and weight k, where N is the conductor, \epsilon is the prime-to-p part of the determinant and k is the so-called minimal weight of \rho. In particular, k=1 if and only if \rho is unramified at p. Direct arguments are used in the exceptional cases, where general results on weight and level lowering are not available. [less ▲]

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