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For arithmetic applications, we extend and refine our previously published results to allow ramifications in a minimal way. Starting with a possibly ramified quadratic extension $F’/F$ of function fields over a finite field in odd characteristic, and a finite set of places $\Sigma $ of $F$ that are unramified in $F’$, we define a collection of Heegner–Drinfeld cycles on the moduli stack of $\mathrm {PGL}_{2}$-Shtukas with $r$-modifications and Iwahori level structures at places of $\Sigma $. For a cuspidal automorphic representation $\pi $ of $\mathrm {PGL}_{2}(\mathbb {A}_{F})$ with square-free level $\Sigma $, and $r\in \mathbb {Z}_{\ge 0}$ whose parity matches the root number of $\pi _{F’}$, we prove a series of identities between
@article{10_4007_annals_2019_189_2_2,
author = {Zhiwei Yun and Wei Zhang},
title = {Shtukas and the {Taylor} expansion of $L$-functions {(II)}},
journal = {Annals of mathematics},
pages = {393--526},
publisher = {mathdoc},
volume = {189},
number = {2},
year = {2019},
doi = {10.4007/annals.2019.189.2.2},
mrnumber = {3919362},
zbl = {07041749},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.2.2/}
}
TY - JOUR AU - Zhiwei Yun AU - Wei Zhang TI - Shtukas and the Taylor expansion of $L$-functions (II) JO - Annals of mathematics PY - 2019 SP - 393 EP - 526 VL - 189 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.2.2/ DO - 10.4007/annals.2019.189.2.2 LA - en ID - 10_4007_annals_2019_189_2_2 ER -
%0 Journal Article %A Zhiwei Yun %A Wei Zhang %T Shtukas and the Taylor expansion of $L$-functions (II) %J Annals of mathematics %D 2019 %P 393-526 %V 189 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.2.2/ %R 10.4007/annals.2019.189.2.2 %G en %F 10_4007_annals_2019_189_2_2
Zhiwei Yun; Wei Zhang. Shtukas and the Taylor expansion of $L$-functions (II). Annals of mathematics, Tome 189 (2019) no. 2, pp. 393-526. doi: 10.4007/annals.2019.189.2.2
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