Results 1 to 10 of about 182 (33)
On Fermat's equation over some quadratic imaginary number fields. [PDF]
Res Number Theory, 2018 Assuming a deep but standard conjecture in the Langlands programme, we prove Fermat's Last Theorem over $\mathbb Q(i)$. Under the same assumption, we also prove that, for all prime exponents $p \geq 5$, Fermat's equation $a^p+b^p+c^p=0$ does not have non-
Ţurcaş GC.
europepmc +4 more sources
ON THE COHOMOLOGY OF TORELLI GROUPS
Forum of Mathematics, Pi, 2020 We completely describe the algebraic part of the rational cohomology of the Torelli groups of the manifolds $\#^{g}S^{n}\times S^{n}$ relative to a disc in a stable range, for $2n\geqslant 6$.
ALEXANDER KUPERS, OSCAR RANDAL-WILLIAMS
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Profinite invariants of arithmetic groups
Forum of Mathematics, Sigma, 2020 We prove that the sign of the Euler characteristic of arithmetic groups with the congruence subgroup property is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself ...
Holger Kammeyer +3 more
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TORSION GALOIS REPRESENTATIONS OVER CM FIELDS AND HECKE ALGEBRAS IN THE DERIVED CATEGORY
Forum of Mathematics, Sigma, 2016 We construct algebras of endomorphisms in the derived category of the cohomology of arithmetic manifolds, which are generated by Hecke operators. We construct Galois representations with coefficients in these Hecke algebras and apply this technique to ...
JAMES NEWTON, JACK A. THORNE
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DERIVED HECKE ALGEBRA AND COHOMOLOGY OF ARITHMETIC GROUPS
Forum of Mathematics, Pi, 2019 We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\unicode[STIX]{x1D6E4}$.
AKSHAY VENKATESH
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COMPACTIFICATIONS OF SUBSCHEMES OF INTEGRAL MODELS OF SHIMURA VARIETIES
Forum of Mathematics, Sigma, 2018 We study several kinds of subschemes of mixed characteristic models of Shimura varieties which admit good (partial) toroidal and minimal compactifications, with familiar boundary stratifications and formal local structures, as if they were Shimura ...
KAI-WEN LAN, BENOÎT STROH
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On the GL$_{n}$-eigenvariety and a conjecture of Venkatesh [PDF]
, 2017 Let π be a cuspidal, cohomological automorphic representation of GL$_{n}$(A). Venkatesh has suggested that there should exist a natural action of the exterior algebra of a certain motivic cohomology group on the π-part of the Betti cohomology (with ...
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An Eisenstein ideal for imaginary quadratic fields and the Bloch-Kato conjecture for Hecke characters [PDF]
, 2007 For certain algebraic Hecke characters chi of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL_2/F.
Agboola +29 more
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Degeneration of Hodge structures over Picard modular surfaces [PDF]
, 2017 We study variations of Hodge structures over a Picard modular surface, and compute the weights and types of their degenerations through the cusps of the Baily-Borel compactification.
Ancona, Giuseppe
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Automorphic forms and rational homology 3–spheres [PDF]
, 2006 We investigate a question of Cooper adjacent to the Virtual Haken Conjecture. Assuming certain conjectures in number theory, we show that there exist hyperbolic rational homology 3–spheres with arbitrarily large injectivity radius.
Calegari, Frank, Dunfield, Nathan M.
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