Tag Archives: RLT

Galois Representations for non self-dual forms, Part II

Posted on April 21, 2013 by Persiflage

(Now with updates!) Let’s recap from part I. We have a Shimura variety \(Y\), a minimal projective compactification \(X\), and a (family of) smooth toroidal compactifications \(W\). We also have Galois representations of the correct shape associated to eigenclasses in … Continue reading →

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Galois Representations for non self-dual forms, Part I

Posted on March 26, 2013 by Persiflage

This is the first of a series of posts discussing the recent work of Harris, Lan, Taylor, and Thorne on constructing Galois representations associated to regular algebraic automorphic forms for \(\mathrm{GL}(n)\) over a CM field \(F/F^{+}\). I will dispense with … Continue reading →

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En Passant

Posted on October 24, 2012 by Persiflage

Several times in NYC, I’ve had the chance to visit Eataly, an italian food court/upscale delicatessen run by Mario Batali. You can either sit down at one of the various restaurants for an antipasto plate with a glass of wine, … Continue reading →

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Remarks on Buzzard-Taylor

Posted on October 18, 2012 by Persiflage

Let \(\rho: G_{\mathbf{Q},S} \rightarrow \mathrm{GL}_2(\overline{\mathbf{Q}}_p)\) be continuous and unramified at \(p\). The Fontaine-Mazur conjecture predicts that \(\rho\) has finite image and is automorphic. Buzzard and Taylor proved this result under the assumption the natural assumption that \(\rho\) is odd, that … Continue reading →

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Why it is good to be Pure

Posted on October 15, 2012 by Persiflage

There do not exist any regular pure motives \(M\) over \(\mathbf{Q}\) which are not essentially self dual. Here is why. \(M\) gives rise to a compatible family of Galois representations for each rational prime \(v\) such that the characteristic polynomial … Continue reading →

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