ترغب بنشر مسار تعليمي؟ اضغط هنا

Local Langlands Conjecture for $p$-adic $GSpin_4,$ $GSpin_6,$ and their inner forms

102   0   0.0 ( 0 )
 نشر من قبل Kwangho Choiy
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We establish the local Langlands conjecture for small rank general spin groups $GSpin_4$ and $GSpin_6$ as well as their inner forms. We construct appropriate $L$-packets and prove that these $L$-packets satisfy the properties expected of them to the extent that the corresponding local factors are available. We are also able to determine the exact sizes of the $L$-packets in many cases.



قيم البحث

اقرأ أيضاً

We construct a Langlands parameterization of supercuspidal representations of $G_2$ over a $p$-adic field. More precisely, for any finite extension $K / QQ_p$ we will construct a bijection [ CL_g : CA^0_g(G_2,K) rightarrow CG^0(G_2,K) ] from the set of generic supercuspidal representations of $G_2(K)$ to the set of irreducible continuous homomorphisms $rho : W_K to G_2(CC)$ with $W_K$ the Weil group of $K$. The construction of the map is simply a matter of assembling arguments that are already in the literature, together with a previously unpublished theorem of G. Savin on exceptional theta correspondences, included as an appendix. The proof that the map is a bijection is arithmetic in nature, and specifically uses automorphy lifting theorems. These can be applied thanks to a recent result of Hundley and Liu on automorphic descent from $GL(7)$ to $G_2$.
330 - D.R. Heath-Brown 2009
A variant of Brauers induction method is developed. It is shown that quartic p-adic forms with at least 9127 variables have non-trivial zeros, for every p. For odd p considerably fewer variables are needed. There are also subsidiary new results concerning quintic forms, and systems of forms.
187 - Binyong Sun 2017
Generalizing the completed cohomology groups introduced by Matthew Emerton, we define certain spaces of ordinary $p$-adic automorphic forms along a parabolic subgroup and show that they interpret all classical ordinary automorphic forms.
We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform results in te rms of local functorial transfers of the generic representations of the groups we consider. The existence of the local transfers follows from global generic transfers that were established earlier.
176 - Ruochuan Liu , Daqing Wan 2016
For a global function field K of positive characteristic p, we show that Artin conjecture for L-functions of geometric p-adic Galois representations of K is true in a non-trivial p-adic disk but is false in the full p-adic plane. In particular, we pr ove the non-rationality of the geometric unit root L-functions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا