Galois representations arising from some compact Shimura varieties

By S. Shin. 2011

195 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d50c93a2c6bae901260edcf2345681fe1f595d54

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Citations in the corpus

Perfectoid Spaces (2011, background): “Let us only mention the work of Taylor and Yoshida, [32], later completed by Shin, [30], and Caraiani, [6], as well as the independent work of Boyer, [4], [5].”
Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “exists and C-algebraic is mapped to C-algebraic). The hypothesis holds with δ= 0. This can be deduced in two ways: By using the work of Arthur [3] to transfer to GL(4) and then applying Shin’s result [96], or by the work of Weissauer [108] and Laumon [73, 74]. (The Conditions 6.4.2, 7.1.2 hold becau”
On the p-adic cohomology of the Lubin-Tate tower (2015, unknown): “There is recent work of Caraiani-Emerton-Gee-GeraghtyPaskunas-Shin, [5], that construct some p-adic GLn(F )-representation starting from an n-dimensional representation of the absolute Galois group of a p-adic field F , for general n and F .”
Potential automorphy and change of weight (2010, background): “Purity can be detected after restricting to GF ′ , and here it follows from the theorem and from the work of Shin [Shi09].”
The stable Bernstein center and test functions for Shimura varieties (2013, methodology): “s. The advantage of what we could call the Langlands-Kottwitz-Scholze approach in this situation is that it yields in [SS] a new construction of the Galois representations constructed earlier by Shin [Sh], in a shorter way that avoids Igusa varieties. In these later developments, Conjecture 6.1.1doe”
Even Galois representations and the Fontaine–Mazur conjecture (2009, background): “If π has slightly regular weight, the the Galois representation associated to π in [Shi10] can be realized geometrically in the étale cohomology of an automorphic sheaf on Sh as considered above.”
On the rigid cohomology of certain Shimura varieties (2014, methodology): “[Sh2] S.-W. Shin, On the cohomological base change for unitary similitude groups, (an appendix to the forthcoming paper by W. Goldring), preprint available at http://math.mit.edu/~swshin/ [So] C. Sorensen, A patching lemma, preprint available at http://fa.institut.math.jussieu.fr/node/45 [T] R. Tayl”
General Serre weight conjectures (2015, methodology): “maximal ideal, for example via [BDJ10, Lem. 2.2]). In particular, for these groups the association of Galois representations (valued in GLn(Qp)) to automorphic representations is well-understood (see [Shi11] and the references therein), and the Taylor–Wiles machinery is also well-developed ([CHT08])”
A geometric perspective on the Breuil–Mézard conjecture (2011, result): “making use of Corollaire 5.3 of [Lab09], Theorem 1.1 of [BLGGT12], and Theorem 4.1.5. (Note that the purity assumption in Theorem 4.1.5 holds by Theorem 1.2 of [Car12], which builds on the results of [Shi11] and [CH11].) We note that our assumptions on v 1 imply that Sλ,τ(U,O)m⊗Zp Qpis free over TT ”
Weight cycling and Serre-type conjectures for unitary groups (2011, methodology): “|F+. Then WD(rπ|G Fw )ss ∼=rec w((πv◦ι −1 w ) ⊗|·| (1−n)/2)ss. 56 MATTHEW EMERTON, TOBY GEE, AND FLORIAN HERZIG Proof. This follows from Lemma 7.1.6, Corollaire 5.3 of [Lab11] and the main results of [Shi11], [CH09], [Car12] and [BLGGT12]. More speciﬁcally, under a mild hypothesis on the weight λ, a”
Iwasawa Main Conjecture for Supersingular Elliptic Curves (2014, background): “Then for some L finite over Qp, there is a Galois representation (by [67], [50] [68]): Rp(π) : GK → GLn(L)”
On torsion in the cohomology of locally symmetric varieties (2013, methodology): “We combine this theorem with the existence of Galois representation ([23], [45], [37], [57], [21]; the precise statement we need is stated as [10, Theorems 1.”
On the automorphy of l-adic Galois representations with small residual image With an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Jack Thorne (2011, background): “At the time of writing this is known to be true, for example, when πv becomes unramified after a finite base change (see [9]) or when π has slightly regular weight in the sense of [35].”