Voir la notice de l'article provenant de la source Cambridge University Press
@article{10_1017_fmp_2019_6,
author = {AKSHAY VENKATESH},
title = {DERIVED {HECKE} {ALGEBRA} {AND} {COHOMOLOGY} {OF} {ARITHMETIC} {GROUPS}},
journal = {Forum of Mathematics, Pi},
publisher = {mathdoc},
volume = {7},
year = {2019},
doi = {10.1017/fmp.2019.6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fmp.2019.6/}
}
AKSHAY VENKATESH. DERIVED HECKE ALGEBRA AND COHOMOLOGY OF ARITHMETIC GROUPS. Forum of Mathematics, Pi, Tome 7 (2019). doi: 10.1017/fmp.2019.6
[1] , , , , , , , , and , ‘Potential automorphy over CM fields’, Preprint, http://math.uchicago.edu/ fcale/papers/Ramanujan.pdf.Google Scholar
[2] and , ‘ L-functions and Tamagawa numbers of motives’, inThe Grothendieck Festschrift, Vol. I, Progress in Mathematics, 86 (Birkhäuser Boston, Boston, MA, 1990), 333–400.Google Scholar
[3] , ‘Stable real cohomology of arithmetic groups’, Ann. Sci. École Norm. Sup. (4) 7 (1974), 235–272.Google Scholar
[4] , ‘Stable real cohomology of arithmetic groups. II’, inManifolds and Lie groups (Notre Dame, Ind., 1980), Progress in Mathematics, 14 (Birkhäuser, Boston, MA, 1981), 21–55.Google Scholar
[5] and , Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, 2nd edn, Mathematical Surveys and Monographs, 67 (American Mathematical Society, Providence, RI, 2000).Google Scholar
[6] , Cohomology of Groups, Graduate Texts in Mathematics, 87 (Springer, New York, 1994), Corrected reprint of the 1982 original.Google Scholar
[7] and , ‘The conjectural connections between automorphic representations and Galois representations’, inAutomorphic Forms and Galois Representations, Vol. 1, London Mathematical Society Lecture Note Series, 414 (Cambridge University Press, Cambridge, 2014), 135–187.Google Scholar
[8] and , ‘Completed cohomology—a survey’, inNon-abelian Fundamental Groups and Iwasawa Theory, London Mathematical Society Lecture Note Series, 393 (Cambridge University Press, Cambridge, 2012), 239–257.Google Scholar
[9] and , ‘Modularity lifting beyond the Taylor-Wiles method’, Invent. Math. 211(1) (2018), 297–433.Google Scholar
[10] and , ‘A torsion Jacquet–Langlands correspondence’, Asterisque (2019), .Google Scholar | arXiv
[11] , , , , , and , ‘Shimura varieties at level and Galois representations’, Preprint, .Google Scholar | arXiv
[12] and , ‘On the Iwahori-Hecke algebra of a p-adic group’, Int. Math. Res. Not. IMRN (2) (1998), 85–100.Google Scholar
[13] , and , ‘Automorphy for some l-adic lifts of automorphic mod l Galois representations’, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 1–181. With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.Google Scholar
[14] and , ‘Derived Galois deformation rings’, Adv. Math. 327 (2018), 470–623.Google Scholar
[15] , ‘Modularity lifting theorems’, Preprint, http://wwwf.imperial.ac.uk/∼tsg/index_files/ArizonaWinterSchool2013.pdf.Google Scholar
[16] , and , ‘Equivariant cohomology, Koszul duality, and the localization theorem’, Invent. Math. 131(1) (1998), 25–83.Google Scholar
[17] and , ‘Derived Hecke algebra for weight one forms’, Exp. Math. 28(3) (2019), 342–361.Google Scholar
[18] and , ‘A cohomological Tamagawa number formula’, Nagoya Math. J. 202 (2011), 45–75.Google Scholar
[19] , ‘On the Lichtenbaum-Quillen conjecture’, inAlgebraic K-Theory and Algebraic Topology (Lake Louise, AB, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 407 (Kluwer Academic Publishers, Dordrecht, 1993), 147–166.Google Scholar
[20] , ‘Homology stability for linear groups’, Invent. Math. 60(3) (1980), 269–295.Google Scholar
[21] and , ‘Potential automorphy and the Leopoldt conjecture’, Amer. J. Math. 139(5) (2017), 1205–1273.Google Scholar
[22] , ‘Automorphic representations, Shimura varieties, and motives. Ein Märchen’, inAutomorphic Forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Part 2, Proceedings of Symposia in Pure Mathematics, XXXIII (American Mathematical Society, Providence, R.I., 1979), 205–246.Google Scholar
[23] , ‘On the motive of an algebraic surface’, J. Reine Angew. Math. 409 (1990), 190–204.Google Scholar
[24] and , ‘A canonical torsion theory for pro-p Iwahori-Hecke modules’, Adv. Math. 327 (2018), 52–127.Google Scholar
[25] and , ‘Automorphic cohomology, motivic cohomology and the adjoint -function’, Preprint, 2016, .Google Scholar | arXiv
[26] , ‘On the cohomology and K-theory of the general linear groups over a finite field’, Ann. of Math. (2) 96 (1972), 552–586.Google Scholar
[27] , ‘A satake homomorphism for the mod Hecke algebra’, Preprint, 2018,.Google Scholar | arXiv
[28] , ‘Smooth representations and Hecke modules in characteristic p ’, Pacific J. Math. 279(1-2) (2015), 447–464.Google Scholar
[29] , ‘Integral elements in K-theory and products of modular curves’, inThe Arithmetic and Geometry of Algebraic Cycles (Banff, AB, 1998), NATO Sci. Ser. C Math. Phys. Sci., 548 (Kluwer Academic Publ., Dordrecht, 2000), 467–489.Google Scholar
[30] , ‘On torsion in the cohomology of locally symmetric varieties’, Ann. of Math. (2) 182(3) (2015), 945–1066.Google Scholar
[31] , ‘Comparison of sheaf cohomology and singular cohomology’, Preprint, 2016,arXiv:1602.06674.Google Scholar
[32] , ‘ K-théorie des anneaux d’entiers de corps de nombres et cohomologie étale’, Invent. Math. 55(3) (1979), 251–295.Google Scholar
[33] , Algebraic K-theory, Modern Birkhäuser Classics, 2nd edn , (Birkhäuser Boston, Inc., Boston, MA, 2008).Google Scholar
[34] , ‘Smith theory and geometric Hecke algebras’, Math. Ann. (2019), .Google Scholar | arXiv
[35] , ‘Cohomology of arithmetic groups and periods of automorphic forms’, Jpn. J. Math. 12(1) (2017), 1–32.Google Scholar
[36] , ‘Étale Chern classes at the prime 2’, inAlgebraic K-Theory and Algebraic Topology (Lake Louise, AB, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 407 (Kluwer Acad. Publ., Dordrecht, 1993), 249–286.Google Scholar
[37] , ‘Note on products in Ext’, Proc. Amer. Math. Soc. 9 (1958), 873–875.Google Scholar
Cité par Sources :