Drinfeld modular polynomials in higher rank II: Kronecker congruences

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• 作者：Florian Breuer^a ; ¹ ; ^{fbreuer@sun.ac.za" class="auth_mail" title="E-mail the corresponding author} ; Hans-Georg Rü ; ck^b ; ^{rueck@mathematik.uni-kassel.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Drinfeld modules ; Modular polynomials ; Isogenies ; Isomorphism invariants
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：165
• 期：Complete
• 页码：1-14
• 全文大小：321 K

文摘

This is a sequel to the paper [4], in which we introduced Drinfeld modular polynomials of higher rank, using an analytic construction. These polynomials relate the isomorphism invariants of Drinfeld class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16000640&_mathId=si1.gif&_user=111111111&_pii=S0022314X16000640&_rdoc=1&_issn=0022314X&md5=1adcc89f5f300f328454c1441993f838" title="Click to view the MathML source">F_q[T]class="mathContainer hidden">class="mathCode">${\mathbb{F}}_q[T]$-modules of rank class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16000640&_mathId=si2.gif&_user=111111111&_pii=S0022314X16000640&_rdoc=1&_issn=0022314X&md5=e34a634461a77b67b28203f2f58d833d" title="Click to view the MathML source">r≥2class="mathContainer hidden">class="mathCode">$r\ge 2$ linked by isogenies of a specified type. In the current paper, we give an algebraic construction of greater generality, and prove a generalization of the Kronecker congruences relations, which describe what happens when modular polynomials associated to P-isogenies are reduced modulo a prime P. We also correct an error in [4].