On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) / / Sophie Morel.
This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois g...
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| Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2010] ©2010 |
| Year of Publication: | 2010 |
| Edition: | Course Book |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
173 |
| Online Access: | |
| Physical Description: | 1 online resource (232 p.) |
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| LEADER | 06470nam a22014175i 4500 | ||
|---|---|---|---|
| 001 | 9781400835393 | ||
| 003 | DE-B1597 | ||
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| 008 | 220131t20102010nju fo d z eng d | ||
| 020 | |a 9781400835393 | ||
| 024 | 7 | |a 10.1515/9781400835393 |2 doi | |
| 035 | |a (DE-B1597)446909 | ||
| 035 | |a (OCoLC)979579419 | ||
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| 100 | 1 | |a Morel, Sophie, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) / |c Sophie Morel. |
| 250 | |a Course Book | ||
| 264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2010] | |
| 264 | 4 | |c ©2010 | |
| 300 | |a 1 online resource (232 p.) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 0 | |a Annals of Mathematics Studies ; |v 173 | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Chapter 1. The fixed point formula -- |t Chapter 2. The groups -- |t Chapter 3. Discrete series -- |t Chapter 4. Orbital integrals at p -- |t Chapter 5. The geometric side of the stable trace formula -- |t Chapter 6. Stabilization of the fixed point formula -- |t Chapter 7. Applications -- |t Chapter 8. The twisted trace formula -- |t Chapter 9. The twisted fundamental lemma -- |t Appendix. Comparison of two versions of twisted transfer factors -- |t Bibliography -- |t Index |
| 506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
| 520 | |a This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group G(Af) of finite adelic points of G. The second action can be studied on the set of complex points of the Shimura variety. In this book, Sophie Morel identifies the Galois action--at good places--on the G(Af)-isotypical components of the cohomology. Morel uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula. The first problem, that of applying the fixed point formula to the intersection cohomology, is geometric in nature and is the object of the first chapter, which builds on Morel's previous work. She then turns to the group-theoretical problem of comparing these results with the trace formula, when G is a unitary group over Q. Applications are then given. In particular, the Galois representation on a G(Af)-isotypical component of the cohomology is identified at almost all places, modulo a non-explicit multiplicity. Morel also gives some results on base change from unitary groups to general linear groups. | ||
| 530 | |a Issued also in print. | ||
| 538 | |a Mode of access: Internet via World Wide Web. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
| 650 | 0 | |a Homology theory. | |
| 650 | 0 | |a Shimura varieties. | |
| 650 | 7 | |a MATHEMATICS / Topology. |2 bisacsh | |
| 653 | |a Accuracy and precision. | ||
| 653 | |a Adjoint. | ||
| 653 | |a Algebraic closure. | ||
| 653 | |a Archimedean property. | ||
| 653 | |a Automorphism. | ||
| 653 | |a Base change map. | ||
| 653 | |a Base change. | ||
| 653 | |a Calculation. | ||
| 653 | |a Clay Mathematics Institute. | ||
| 653 | |a Coefficient. | ||
| 653 | |a Compact element. | ||
| 653 | |a Compact space. | ||
| 653 | |a Comparison theorem. | ||
| 653 | |a Conjecture. | ||
| 653 | |a Connected space. | ||
| 653 | |a Connectedness. | ||
| 653 | |a Constant term. | ||
| 653 | |a Corollary. | ||
| 653 | |a Duality (mathematics). | ||
| 653 | |a Existential quantification. | ||
| 653 | |a Exterior algebra. | ||
| 653 | |a Finite field. | ||
| 653 | |a Finite set. | ||
| 653 | |a Fundamental lemma (Langlands program). | ||
| 653 | |a Galois group. | ||
| 653 | |a General linear group. | ||
| 653 | |a Haar measure. | ||
| 653 | |a Hecke algebra. | ||
| 653 | |a Homomorphism. | ||
| 653 | |a L-function. | ||
| 653 | |a Logarithm. | ||
| 653 | |a Mathematical induction. | ||
| 653 | |a Mathematician. | ||
| 653 | |a Maximal compact subgroup. | ||
| 653 | |a Maximal ideal. | ||
| 653 | |a Morphism. | ||
| 653 | |a Neighbourhood (mathematics). | ||
| 653 | |a Open set. | ||
| 653 | |a Parabolic induction. | ||
| 653 | |a Permutation. | ||
| 653 | |a Prime number. | ||
| 653 | |a Ramanujan-Petersson conjecture. | ||
| 653 | |a Reductive group. | ||
| 653 | |a Ring (mathematics). | ||
| 653 | |a Scientific notation. | ||
| 653 | |a Shimura variety. | ||
| 653 | |a Simply connected space. | ||
| 653 | |a Special case. | ||
| 653 | |a Sub"ient. | ||
| 653 | |a Subalgebra. | ||
| 653 | |a Subgroup. | ||
| 653 | |a Symplectic group. | ||
| 653 | |a Theorem. | ||
| 653 | |a Trace formula. | ||
| 653 | |a Unitary group. | ||
| 653 | |a Weyl group. | ||
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Backlist 2000-2013 |z 9783110442502 |
| 776 | 0 | |c print |z 9780691142937 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400835393 |
| 856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400835393 |
| 856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400835393/original |
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