Shimura Subgroups and Degeneracy Maps

✍ Scribed by S. Ling

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 680 KB
• Volume: 54
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1995.1100

✦ Synopsis

For (M \geqslant 1) an integer and (M^{\prime}) a positive divisor of (M), let (\phi: J_{01}\left(M^{\prime}\right)^{\top} \rightarrow J_{0}(M)) be the map defined by all the degeneracy maps, where (t) is the number of positive divisors of (M / M^{\prime}). We determine the kernel of (\phi) for certain (M) and (M^{\prime}), as well as relate the pre-image of the Shimura subgroup (\Sigma(M)) under (\phi) to the group (\Sigma\left(M^{\prime}\right)^{\text {r }}). We also study the restriction of degeneracy maps to Shimura subgroups. 1995 Academic Press, Inc