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## 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. document.getElementById('cloakdece9d3a9babf61420173952b0cf2c50').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addydece9d3a9babf61420173952b0cf2c50 = 'h&#101;ct&#111;r.m&#97;th' + '&#64;'; addydece9d3a9babf61420173952b0cf2c50 = addydece9d3a9babf61420173952b0cf2c50 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_textdece9d3a9babf61420173952b0cf2c50 = 'h&#101;ct&#111;r.m&#97;th' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloakdece9d3a9babf61420173952b0cf2c50').innerHTML += '<a ' + path + '\'' + prefix + ':' + addydece9d3a9babf61420173952b0cf2c50 + '\'>'+addy_textdece9d3a9babf61420173952b0cf2c50+'<\/a>';

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).