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作者：Khare, Chandrashekhar; Wintenberger, Jean-Pierre
摘要：We prove the existence in many cases of minimally ramified p-adic lifts of 2-dimensional continuous, odd, absolutely irreducible, mod p representations (rho) over bar of the absolute Galois group of Q. It is predicted by Serre's conjecture that such representations arise from newforms of optimal level and weight. Using these minimal lifts, and arguments using compatible systems, we prove some cases of Serre's conjectures in low levels and weights. For instal-ice we prove that there are no irre...
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作者：Calegari, Frank; Emerton, Matthew
摘要：Let G(infinity) be a semisimple real Lie group with unitary dual (G) over cap (infinity). We produce new upper bounds for the multiplicities with which representations pi is an element of (G) over cap (infinity) of cohomological type appear in certain spaces of cusp forms on G(infinity). The main new idea is to apply noncommutative Iwasawa theory to certain p-adic completions of the cohomology of locally symmetric spaces.
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作者：Frenkel, Edward; Gaitsgory, Dennis
摘要：We consider the category of modules over the affine Kac-Moody algebra g of critical level with regular central character. In our previous paper we conjectured that this category is equivalent to the category of Hecke eigen-D-modules on the affine Grassmannian G((t))/G[[t]]. This conjecture was motivated by our proposal for a local geometric Langlands correspondence. In this paper we prove this conjecture for the corresponding I-0 equivariant categories, where I-0 is the radical of the Iwahori ...
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作者：Vogel, Thomas
摘要：We develop a construction of Engel structures on 4-manifolds based on decompositions of manifolds into round handles. This allows us to show that all parallelizable 4-manifolds admit an Engel structure. We also show that, given two Engel manifolds M-1, M-2 satisfying a certain condition on the characteristic foliations, there is an Engel structure on M-1#M-2#(S-2 x S-2) which is closely related to the original Engel structures.
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作者：Brosnan, Patrick; Pearlstein, Gregory J.
摘要：We prove that the zero locus of an admissible normal function over an algebraic parameter space S is algebraic in the case where S is a curve.
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作者：Getzler, Ezra
摘要：The Deligne groupoid is a functor from nilpotent differential graded Lie algebras concentrated in positive degrees to groupoids; in the special case of Lie algebras over a field of characteristic zero, it gives the associated simply connected Lie group. We generalize the Deligne groupoid to a functor gamma from L-infinity-algebras concentrated in degree > -n to n-groupoids. (We actually construct the nerve of the n-groupoid, which is an enriched Kan complex.) The construction of gamma is quite...
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作者：Ringstrom, Hans
摘要：Einstein's vacuum equations can be viewed as an initial value problem, and given initial data there is one part of spacetime, the so-called maximal globally hyperbolic development (MGHD), which is uniquely determined up to isometry. Unfortunately, it is sometimes possible to extend the spacetime beyond the MGHD in inequivalent ways. Consequently, the initial data do not uniquely determine the spacetime, and in this sense the theory is not deterministic. It is then natural to make the strong co...
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作者：Shalev, Aner
摘要：Let w = w (x(1), ..., x(d)) not equal 1 be a nontrivial group word. We show that if G is a sufficiently large finite simple group, then every element g is an element of G can be expressed as a product of three values of w in G. This improves many known results for powers, commutators, as well as a theorem on general words obtained in [19]. The proof relies on probabilistic ideas, algebraic geometry, and character theory. Our methods, which apply the 'zeta function' zeta G(s) = Sigma(chi is an ...
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作者：Paran, Elad
摘要：We prove that every finite split embedding problem is solvable over the field K((X-1,..., X-n)) of formal power series in n >= 2 variables over an arbitrary field K, as well as over the field Quot(A [[X-1,..., Xn]]) of formal power series in n >= 1 variables over a Noetherian integrally closed domain A. This generalizes a theorem of Harbater and Stevenson, who settled the case K((X-1, X-2)).
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作者：Lichtenbaum, Stephen
摘要：There should be a Grothendieck topology for an arithmetic scheme X such that the Euler characteristic of the cohomology groups of the constant sheaf Z with compact support at infinity gives, up to sign, the leading term of the zeta-function of X at s = 0. We construct a topology (the Weil-etale topology) for the ring of integers in a number field whose cohomology groups H-i (Z) determine such an Euler characterstic if we restrict to i <= 3.
