Matches in SemOpenAlex for { <https://semopenalex.org/work/W3201486997> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W3201486997 endingPage "247" @default.
- W3201486997 startingPage "203" @default.
- W3201486997 abstract "Stevens’s overconvergent modular symbols can replace Coleman’s overconvergent modular forms in the construction of the eigencurve. We give in Sect. 7.1 a detailed version of this construction. We then (Sect. 7.2) use Chenevier’s comparison theorem (see Sect. 3.8) to prove that this eigencurve is essentially the same as the Coleman-Mazur eigencurve. This construction provides over the eigencurve a natural module of distribution-valued modular symbols which is closely related to L-functions. In the next Sect. 7.3, we offer a detailed discussion of the points of the eigencurve that correspond to classical modular forms. Those points, and their neighborhoods in the eigencurve, are the main objects of interest for arithmetical applications. Section 7.4 introduces and studies one of the last remaining important characters of our intrigue, the family of Galois representations that the eigencurve carry. Using this family and Galois cohomology arguments, we study the local geometry of the eigencurve at classical points, focussing on questions of smoothness and etaleness over the weight space. Finally, we briefly discuss the most important results and questions concerning the global geometry of the eigencurve." @default.
- W3201486997 created "2021-09-27" @default.
- W3201486997 creator A5083891230 @default.
- W3201486997 date "2021-01-01" @default.
- W3201486997 modified "2023-10-16" @default.
- W3201486997 title "The Eigencurve of Modular Symbols" @default.
- W3201486997 cites W1496632731 @default.
- W3201486997 cites W1516360539 @default.
- W3201486997 cites W172805472 @default.
- W3201486997 cites W1877547708 @default.
- W3201486997 cites W1975475886 @default.
- W3201486997 cites W1998812755 @default.
- W3201486997 cites W2002171490 @default.
- W3201486997 cites W2010146289 @default.
- W3201486997 cites W2023388055 @default.
- W3201486997 cites W2027627786 @default.
- W3201486997 cites W2035591380 @default.
- W3201486997 cites W2075141681 @default.
- W3201486997 cites W2079848363 @default.
- W3201486997 cites W2141954349 @default.
- W3201486997 cites W2143350370 @default.
- W3201486997 cites W2156217705 @default.
- W3201486997 cites W2327344194 @default.
- W3201486997 cites W2345082785 @default.
- W3201486997 cites W2389278099 @default.
- W3201486997 cites W2504050845 @default.
- W3201486997 cites W2765598095 @default.
- W3201486997 cites W2776694140 @default.
- W3201486997 cites W2951785495 @default.
- W3201486997 cites W2962852560 @default.
- W3201486997 cites W3103393767 @default.
- W3201486997 cites W3105511666 @default.
- W3201486997 cites W3151463332 @default.
- W3201486997 cites W329009470 @default.
- W3201486997 cites W2063812109 @default.
- W3201486997 doi "https://doi.org/10.1007/978-3-030-77263-5_7" @default.
- W3201486997 hasPublicationYear "2021" @default.
- W3201486997 type Work @default.
- W3201486997 sameAs 3201486997 @default.
- W3201486997 citedByCount "0" @default.
- W3201486997 crossrefType "book-chapter" @default.
- W3201486997 hasAuthorship W3201486997A5083891230 @default.
- W3201486997 hasConcept C101468663 @default.
- W3201486997 hasConcept C199360897 @default.
- W3201486997 hasConcept C41008148 @default.
- W3201486997 hasConceptScore W3201486997C101468663 @default.
- W3201486997 hasConceptScore W3201486997C199360897 @default.
- W3201486997 hasConceptScore W3201486997C41008148 @default.
- W3201486997 hasLocation W32014869971 @default.
- W3201486997 hasOpenAccess W3201486997 @default.
- W3201486997 hasPrimaryLocation W32014869971 @default.
- W3201486997 hasRelatedWork W2093578348 @default.
- W3201486997 hasRelatedWork W2177563685 @default.
- W3201486997 hasRelatedWork W2358668433 @default.
- W3201486997 hasRelatedWork W2376932109 @default.
- W3201486997 hasRelatedWork W2382290278 @default.
- W3201486997 hasRelatedWork W2390279801 @default.
- W3201486997 hasRelatedWork W2748952813 @default.
- W3201486997 hasRelatedWork W2888805005 @default.
- W3201486997 hasRelatedWork W2899084033 @default.
- W3201486997 hasRelatedWork W4238335261 @default.
- W3201486997 isParatext "false" @default.
- W3201486997 isRetracted "false" @default.
- W3201486997 magId "3201486997" @default.
- W3201486997 workType "book-chapter" @default.