Pramod N. Achar

main research teaching resources

Preprints

[7]

(with S. Riche) Reductive groups, the loop Grassmannian, and the Springer resolution.

arXiv | hal

[6]

Corrigendum to “On the equivariant K-theory of the nilpotent cone in the general linear group.”

arXiv

[5]

(with A. Henderson, D. Juteau, and S. Riche) Modular generalized Springer correspondence: an overview.

arXiv | hal

[4]

(with A. Henderson, D. Juteau, and S. Riche) Constructible sheaves on nilpotent cones in rather good characteristic.

arXiv | hal

[3]

(with A. Henderson, D. Juteau, and S. Riche) Modular generalized Springer correspondence III: exceptional groups.

arXiv | hal

[2]

(with L. Rider, and an appendix joint with S. Riche) The affine Grassmannian and the Springer resolution in positive characteristic.

pdf | arXiv

[1]

(with S. Riche) Modular perverse sheaves on flag varieties III: positivity conditions.

pdf | arXiv | hal

Articles in press

[3]

(with A. Henderson, D. Juteau, and S. Riche) Modular generalized Springer correspondence II: classical groups.

J. Eur. Math. Soc. (JEMS), to appear.

arXiv | hal

[2]

(with S. Riche, and a joint appendix with G. Williamson) Modular perverse sheaves on flag varieties I: tilting and parity sheaves.

Ann. Sci. Éc. Norm. Supér., to appear.

arXiv | hal

[1]

(with A. Henderson, D. Juteau, and S. Riche) Modular generalized Springer correspondence I: the general linear group.

J. Eur. Math. Soc. (JEMS), to appear.

arXiv | hal

Published papers

[34]

(with S. Riche) Modular perverse sheaves on flag varieties II: Koszul duality and formality.

Duke Math. J. 165 (2016), 161–215.

doi | arXiv | hal

[33]

(with L. Rider) Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture.

Acta Math. 215 (2015), 183–216.

doi | arXiv

[32]

(with C. Mautner) Sheaves on nilpotent cones, Fourier transform, and a geometric Ringel duality.

Mosc. Math. J. 15 (2015), 407–423.

journal | arXiv

[31]

On exotic and perverse-coherent sheaves.

Representations of reductive groups: in honor of the 60th birthday of David A. Vogan, Jr. (M. Nevins and P. E. Trapa, eds.), Progr. Math., vol. 312, Birkhäuser/Springer, 2015, pp. 11–49.

doi | arXiv

[30]

(with A. Henderson and S. Riche) Geometric Satake, Springer correspondence, and small representations II.

Represent. Theory 19 (2015), 94–166.

doi | arXiv | hal

[29]

(with S. Riche) Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone.

Israel J. Math. 205 (2015), 247–315.

doi | arXiv | hal

[28]

(with S. Kitchen) Koszul duality and mixed Hodge modules.

Int. Math. Res. Not. IMRN 2014, 5874–5911.

doi | arXiv

[27]

(with A. Henderson, D. Juteau, and S. Riche) Weyl group actions on the Springer sheaf.

Proc. Lond. Math. Soc. 108 (2014), 1501–1528.

doi | arXiv | hal

[26]

Kostka systems and exotic t-structures for reflection groups.

Recent developments in algebraic and combinatorial aspects of representation theory, Contemp. Math. 602 (2013), 1–21.

doi | arXiv

[25]

(with S. Riche) Koszul duality and semisimplicity of Frobenius.

Ann. Inst. Fourier 63 (2013), 1511–1612.

doi | arXiv | hal

[24]

(with A. Henderson) Geometric Satake, Springer correspondence, and small representations.

Selecta Math. 19 (2013), 949–986.

doi | arXiv

[23]

(with C. Stroppel) Completions of Grothendieck groups.

Bull. Lond. Math. Soc. 45 (2013), 200–212.

doi | arXiv

[22]

Perverse coherent sheaves on the nilpotent cone in good characteristic.

Recent developments in Lie algebras, groups and representation theory, Proc. Symp. Pure Math. 86 (2012), 1–23.

doi | arXiv

[21]

(with D. Treumann) Purity and decomposition theorems for staggered sheaves.

J. Inst. Math. Jussieu 11 (2012), 695–745.

doi | arXiv

[20]

Green functions via hyperbolic localization.

Doc. Math. 16 (2011), 869–884.

journal | arXiv

[19]

(with A. Henderson and B. Jones) Normality of orbit closures in the enhanced nilpotent cone.

Nagoya Math. J. 203 (2011), 1–45.

doi | arXiv

[18]

(with D. Treumann) Baric structures on triangulated categories and coherent sheaves.

Int. Math. Res. Not. IMRN 2011, 3688–3743.

doi | arXiv

[17]

(with A. Henderson and E. Sommers) Pieces of nilpotent cones for classical groups.

Represent. Theory 15 (2011), 584–616.

doi | arXiv

[16]

(with C. Cunningham) Toward a Mackey formula for compact restriction of character sheaves.

Harmonic analysis on reductive, p-adic groups, Contemp. Math. 543 (2011), 1–18.

doi | arXiv

[15]

(with A.-M. Aubert) Localisation de faisceaux caractères.

Adv. Math. 224 (2010), 2435–2471.

doi | arXiv

[14]

On the quasi-hereditary property for staggered sheaves.

Trans. Amer. Math. Soc. 362 (2010), 4735–4753.

doi | arXiv

[13]

Springer theory for complex reflection groups.

組合せ論的表現論の拡がり [Expansion of combinatorial representation theory], 数理解析研究所講究録 [RIMS Kôkyûroku] no. 1647 (2009), 97–112.

journal | pdf

[12]

Staggered t-structures on derived categories of equivariant coherent sheaves.

Int. Math. Res. Not. IMRN 2009, 3843–3900.

doi | arXiv

[11]

(with D. S. Sage) Staggered sheaves on partial flag varieties.

C. R. Math. Acad. Sci. Paris, Ser. I 347 (2009), 139–142.

doi | arXiv

[10]

(with D. S. Sage) Perverse coherent sheaves and the geometry of special pieces in the unipotent variety.

Adv. Math. 220 (2009), 1265–1296.

doi | arXiv | IHÉS

[9]

(with D. S. Sage) On special pieces, the Springer correspondence, and unipotent characters.

Amer. J. Math. 130 (2008), 1399–1425.

doi | arXiv

[8]

(with A. Henderson) Orbit closures in the enhanced nilpotent cone.

Adv. Math. 219 (2008), 27–62.

doi | arXiv

Corrigendum. Adv. Math. 228 (2011), 2984–2988.

doi | arXiv

[7]

(with A.-M. Aubert) Springer correspondences for dihedral groups.

Transform. Groups 13 (2008), 1–24.

doi | arXiv

[6]

(with A.-M. Aubert) On rank 2 complex reflection groups.

Comm. Algebra 36 (2008), 2092–2132.

doi | pdf | prépub. Jussieu

[5]

(with A.-M. Aubert) Représentations de Springer pour les groupes de réflexions complexes imprimitifs.

J. Algebra 319 (2008), 4102–4139.

doi | arXiv

[4]

(with A.-M. Aubert) Supports unipotents de faisceaux caractères.

J. Inst. Math. Jussieu 6 (2007), 173–207.

doi | arXiv | prépub. Jussieu

[3]

On the equivariant K-theory of the nilpotent cone in the general linear group.

Represent. Theory 8 (2004), 180–211.

doi | pdf

[2]

An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient.

Transform. Groups 8 (2003), 107–145.

doi | arXiv

[1]

(with E. Sommers) Local systems on nilpotent orbits and weighted Dynkin diagrams.

Represent. Theory 6 (2002), 190–201.

doi | arXiv

Unpublished manuscripts

[4]

Equivariant mixed Hodge modules.

Lecture notes from the CMI workshop on Mixed Hodge Modules and Applications, 2013.

pdf

[3]

Introduction to staggered sheaves.

Preprint, 2008.

arXiv

[2]

Equivariant coherent sheaves on the nilpotent cone for complex reductive Lie groups.

Ph.D. Thesis, Massachusetts Institute of Technology, 2001.

DSpace | pdf

[1]

Generalized conjugacy classes.

Rose–Hulman Mathematical Sciences Technical Report Series no. 97–01, 1997.

MSTR | pdf