Results 1 to 10 of about 32 (19)

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups

, 2011
We discuss the construction of totally geodesic cycles in locally symmetric spaces attached to arithmetic subgroups in algebraic groups G of type F4 which originate with reductive subgroups of the group G. In many cases, it can be shown that these cycles,
J. Schwermer
semanticscholar   +1 more source

Interpolating coefficient systems and $p$-ordinary cohomology of arithmetic groups

, 2011
We present an approach to Hida’s theory of p-adically interpolating the ordinary cohomology of arithmetic groups and we discuss some application of this approach to special values of L-functions. Mathematics Subject Classification (2010).
G. Harder
semanticscholar   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Higher order invariants in the case of compact quotients

Open Mathematics, 2011
Deitmar Anton
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