Results 1 to 10 of about 36 (36)

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, Steffen Kionke, Jean Raimbault, Roman Sauer   +3 more
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On the non-vanishing of the first Betti number of hyperbolic three manifolds [PDF]

, 2004
. We show the non-vanishing of cohomology groups of sufficiently small congruence lattices in SL(1,D), where D is a quaternion division algebra defined over a number field E contained inside a solvable extension of a totally real number field.As a ...
Rajan, C. S., C. S. Rajan
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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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Rigid meromorphic cocycles for orthogonal groups

Forum of Mathematics, Sigma
Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real signature and constructed in some instances via a p-adic analogue of Borcherds’ singular theta lift.
Lennart Gehrmann, Henri Darmon, Michael Lipnowski   +2 more
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L-invariants for cohomological representations of PGL(2) over arbitrary number fields

Forum of Mathematics, Sigma
Let $\pi $ be a cuspidal, cohomological automorphic representation of an inner form G of $\operatorname {{PGL}}_2$ over a number field F of arbitrary signature. Further, let $\mathfrak {p}$ be a prime of F such that G is split at
Lennart Gehrmann, Maria Rosaria Pati
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Eisenstein Cohomology for $\mathrm {GL}_N$ and the special values of Rankin–Selberg L-functions over a totally imaginary number field

Forum of Mathematics, Sigma
This article presents new rationality results for the ratios of critical values of Rankin–Selberg L-functions of $\mathrm {GL}(n) \times \mathrm {GL}(n')$ over a totally imaginary field $F.$ The proof is based on a cohomological ...
A. Raghuram
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Cohomologie de GL_2(Z[i,1/2]) à coefficients dans F_2

, 2007
Classification AMS :11F75, 20J06, 55T10, 55N25The aim of this Phd thesis was to compute H*(BGL_2(Z[i,1/2]),F_2). This cohomology ring appears in a certain version of the conjecture of Lichtenbaum and Quillen, asserting that the cohomology modulo 2 of the
Weiss, Nicolas
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