A geometric proof of the Feigin-Frenkel theorem

Raskin, Sam

doi:10.1090/s1088-4165-2012-00417-4

Cited by 1 publication

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The key fact we will need from commutative algebra is that a prime ideal in any (possibly infinitely generated) polynomial algebra over a Noetherian ring (e.g., k) is finitely generated if and only if it has finite height (in the usual sense of commutative algebra). Indeed, this result is essentially given by [GH] Theorem 4 (see also [Ras1] Proposition 4.3, which completes the argument in some simple respects). 27 Let J Ď Brtx i u iPI 2 s be the ideal of the closed embedding.…”

Section: Proof For (1)supporting

confidence: 55%

On the notion of spectral decomposition in local geometric Langlands

Raskin

2015

Preprint

Self Cite

View full text Add to dashboard Cite

The geometric Langlands program is distinguished in assigning spectral decompositions to all representations, not only the irreducible ones. However, it is not even clear what is meant by a spectral decomposition when one works with non-abelian reductive groups and with ramification. The present work is meant to clarify the situation, showing that the two obvious candidates for such a notion coincide.More broadly, we study the moduli space of (possibly irregular) de Rham local systems from the perspective of homological algebra. We show that, in spite of its infinite-dimensional nature, this moduli space shares many of the nice features of an Artin stack. Less broadly, these results support the belief in the existence of a version of geometric Langlands allowing arbitrary ramification.Along the way, we give some apparently new, if unsurprising, results about the algebraic geometry of the moduli space of connections, using Babbitt-Varadarajan's reduction theory for differential equations.

show abstract

Section: Proof For (1)supporting

confidence: 55%