Cohomology of Arithmetic Groups
The objects of concern in this book are the sheaf-cohomology groups of locally symmetric spaces attached to arithmetically defined groups Γ, contained in an algebraic group. The sheaves are associated to Γ-modules over the ring of integers or finite extension rings thereof. There is an action of a H...
Gorde:
| Egile nagusia: | |
|---|---|
| Erakunde egilea: | |
| Formatua: | Baliabide elektronikoa eBook |
| Hizkuntza: | ingelesa |
| Argitaratua: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
|
| Edizioa: | 1st ed. 2025. |
| Saila: | Springer Monographs in Mathematics,
|
| Gaiak: | |
| Sarrera elektronikoa: | https://doi.org/10.1007/978-3-032-10378-9 |
| Etiketak: |
Etiketa erantsi
Etiketarik gabe, Izan zaitez lehena erregistro honi etiketa jartzen!
|
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-032-10378-9 | ||
| 003 | DE-He213 | ||
| 005 | 20260810115208.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 260102s2025 sz | o |||| 0|eng d | ||
| 020 | |a 9783032103789 |9 978-3-032-10378-9 | ||
| 024 | 7 | |a 10.1007/978-3-032-10378-9 |2 doi | |
| 050 | 4 | |a QA1-939 | |
| 072 | 7 | |a PB |2 bicssc | |
| 072 | 7 | |a MAT000000 |2 bisacsh | |
| 072 | 7 | |a PB |2 thema | |
| 082 | 0 | 4 | |a 510 |2 23 |
| 100 | 1 | |a Harder, Günter. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Cohomology of Arithmetic Groups |h [electronic resource] / |c by Günter Harder. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XVIII, 284 p. 5 illus.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
| 341 | 0 | |b Use of color is not sole means of conveying information |2 onix | |
| 341 | 0 | |b Use of high contrast between text and background color |2 onix | |
| 341 | 0 | |b Next / Previous structural navigation |2 onix | |
| 341 | 0 | |b All non-decorative content supports reading without sight |2 onix | |
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Springer Monographs in Mathematics, |x 2196-9922 | |
| 505 | 0 | |a 1 Basic Notions and Definitions -- 2 The Cohomology Groups -- 3 Hecke Operators -- 4 Representation Theory -- 5 Applications to Number Theory -- 6 Analytic Methods. | |
| 520 | |a The objects of concern in this book are the sheaf-cohomology groups of locally symmetric spaces attached to arithmetically defined groups Γ, contained in an algebraic group. The sheaves are associated to Γ-modules over the ring of integers or finite extension rings thereof. There is an action of a Hecke algebra on these cohomology groups. Accordingly, they decompose into indecomposable pieces which are of great interest in number theory and algebraic geometry. Upon extending the coefficient systems to complex vector spaces, an individual indecomposable component corresponds to a space of automorphic forms, thereby, giving rise to an attached L-function. For example, the Ramanujan Delta function provides the first case of such a correspondence. Up to division by a carefully chosen period, these L-functions take rational (algebraic) values at certain critical arguments. In various examples, it is discussed how the numerator and denominator ideals of these normalised values shed some light on the integral structure of the cohomology groups as a module under the Hecke algebra. In particular, results concern the denominator of cohomology classes which are represented by Eisenstein series, analytically constructed beforehand. In very special cases, values of the Riemann zeta-function play a decisive role. Within the discussion of these number-theoretic aspects of the cohomology groups, questions of a computational nature unfold. These may lead, by means of experiments, to a better understanding of the general integral structure of these groups. This introduction to the cohomology of arithmetic groups and the associated theory of automorphic forms and special values of L-functions focuses on number theoretic aspects and questions. It is intended for graduate students and researchers in the field of arithmetic as well as in automorphic forms and differential geometry. | ||
| 532 | 8 | |a Accessibility summary: This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, described non-text content (images, graphs), bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Mathematics. | |
| 650 | 1 | 4 | |a Mathematics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783032103772 |
| 776 | 0 | 8 | |i Printed edition: |z 9783032103796 |
| 776 | 0 | 8 | |i Printed edition: |z 9783032103802 |
| 830 | 0 | |a Springer Monographs in Mathematics, |x 2196-9922 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-032-10378-9 |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 912 | |a ZDB-2-251 | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||
| 950 | |a Focus Bundle Mathematics and Statistics (SpringerNature-85421) | ||