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**1 - 4**of**4**### Serre’s modularity conjecture (II)

, 2007

"... We provide proofs of Theorems 4.1 and 5.1 of [30]. ..."

by O Zariski, P Samuel

Venue: | Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh |

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by
Chandrashekhar Khare, Jean-Pierre Wintenberger
, 2007

"... We provide proofs of Theorems 4.1 and 5.1 of [30]. ..."

by
Francesc Planas-vilanova, Rafael, H. Villarreal

"... ar ..."

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...lary 8.9). For all unexplained terminology and additional information, we refer to [10, 27, 36] (for the theory of binomial and lattice ideals), [9, 15] (for Gröbner bases and Hilbert functions) and =-=[5, 25, 38]-=- (for commutative algebra). 2. Preliminaries In this section, we present some of the results that will be needed throughout the paper and introduce some more notation. All results of this section are ...

by
Francesc Planas-vilanova

"... ar ..."

by
Heather Russell
, 2000

"... ..."

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... a generic curve with the condition corresponding to I with respect to the blow up of S at the singular point of the curve is the condition corresponding to the quadratic transform of I as defined in =-=[15]-=-. In particular, given a sequence of positive integers n1, . . .,nr, the condition corresponding to I(n1, . . .,nr) is the closure of the condition of having an r th order point such that if y is a lo...

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