2026/04/01 by María Inés de Frutos-Fernández, Daniel Macías Castillo, Daniel Macias Castillo +1
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation
paper · doi:10.1017/s0010437x26103108
Abstract Let upper K divided by k <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mi>K</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>k</mml:mi> </mml:math> K/k be a finite Galois extension of global function fields. Let E be a Drinfeld module over k . We state and prove an equivariant refinement of Taelman’s analogue of the analytic class number formula for left parenthesis upper E comma upper K divided by k right parenthesis <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>E</mml:mi> <mml:mo>,</mml:mo> <mml:mi>K</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>k</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> (E,K/k) , and derive explicit consequences for the Galois structure of the Taelman class group of E over K .