ENG 
ESP Session S21 - Galois representations and automorphic forms
No date set.
Langlands Functoriality Conjecture for $SO_{2n}^*$ in positive characteristic.
Héctor del Castillo
Pontificia Universidad Católica de Valparaíso , Chile - This email address is being protected from spambots. You need JavaScript enabled to view it.
In [1,2] Cogdell, Kim, Piateski-Shapiro and Shahidi prove Langlands functioriality conjecture for globally generic cuspidal automorphic representations from the split classical groups, unitary groups or even quasi-split special orthogonal groups to the general linear groups. They have done this in the context of characteristic zero. Later, Lomelí in [4,5] extends this result to split classical groups and unitary groups in positive characteristic. In this poster we will discuss functoriality conjecture in the globally generic case for the even quasi-split non-split special orthogonal groups in positive characteristic and some of its applications [3].
$\textbf{References}$.
[1] James W. Cogdell, Ilya I. Piatetski-Shapiro and Freydoon Shahidi. $\textit{Functoriality for the classical groups}$. Publications Mathématiques de l'IHÉS, Volume 99, pp. 163-233 (2004).
[2] James W. Cogdell, Ilya I. Piatetski-Shapiro and Freydoon Shahidi. $\textit{Functoriality for the Quasisplit}$ $ \textit{Classical Groups}$. On Certain L-Functions. Clay Mathematics Proceedings Vol. 13, pp. 117-140 (2011).
[3] Héctor del Castillo. $\textit{Langlands Functoriality Conjecture for $SO_{2n}^*$ in positive characteristic}$. Ph.D. thesis.
[4] Luis Lomelí. $\textit{Functoriality for the Classical Groups over Function Fields}$. International Mathematics Research Notices, Volume 2009, Issue 22, pp. 4271–4335 (2009).
[5] Luis Lomelí. $\textit{Rationality and holomorphy of Langlands–Shahidi L-functions over function fields}$. Mathematische Zeitschrift 291 (1-2), pp. 711-739 (2019).