Singularities of local models
We construct local models of Shimura varieties and investigate their singularities, with
special emphasis on wildly ramified cases. More precisely, with the exception of odd unitary …
special emphasis on wildly ramified cases. More precisely, with the exception of odd unitary …
Generalized juggling patterns, quiver Grassmannians and affine flag varieties
E Feigin, M Lanini, A Pütz - Mathematische Zeitschrift, 2024 - Springer
The goal of this paper is to clarify the connection between certain structures from the theory
of totally nonnegative Grassmannians, quiver Grassmannians for cyclic quivers and the …
of totally nonnegative Grassmannians, quiver Grassmannians for cyclic quivers and the …
On the moduli description of ramified unitary Local models of signature (n-1, 1)
Y Luo - arXiv preprint arXiv:2404.10723, 2024 - arxiv.org
We give a moduli description for the ramified unitary local model of signature (n-1, 1) with
any parahoric level structure when the residue field has characteristic not equals 2 …
any parahoric level structure when the residue field has characteristic not equals 2 …
[HTML][HTML] Laumon parahoric local models via quiver Grassmannians
E Feigin, M Lanini, A Pütz - Journal of Pure and Applied Algebra, 2025 - Elsevier
Local models of Shimura varieties in type A can be realized inside products of
Grassmannians via certain linear algebraic conditions. Laumon suggested a generalization …
Grassmannians via certain linear algebraic conditions. Laumon suggested a generalization …
Symplectic Grassmannians and cyclic quivers
E Feigin, M Lanini, M Micheli, A Pütz - Annali di Matematica Pura ed …, 2024 - Springer
The goal of this paper is to extend the quiver Grassmannian description of certain
degenerations of Grassmann varieties to the symplectic case. We introduce a symplectic …
degenerations of Grassmann varieties to the symplectic case. We introduce a symplectic …
Semi-stable and splitting models for unitary Shimura varieties over ramified places. II
I Zachos, Z Zhao - arXiv preprint arXiv:2405.06163, 2024 - arxiv.org
We consider Shimura varieties associated to a unitary group of signature $(n-1, 1) $. For
these varieties, we construct $ p $-adic integral models over odd primes $ p $ which ramify …
these varieties, we construct $ p $-adic integral models over odd primes $ p $ which ramify …
Semi-stable models for some unitary Shimura varieties over ramified primes
I Zachos - arXiv preprint arXiv:2210.14043, 2022 - arxiv.org
We consider Shimura varieties associated to a unitary group of signature $(2, n-2) $. We
give regular $ p $-adic integral models for these varieties over odd primes $ p $ which ramify …
give regular $ p $-adic integral models for these varieties over odd primes $ p $ which ramify …
Semi-stable models for unitary Shimura varieties over ramified places. I. The even dimensional case
I Zachos, Z Zhao - arXiv preprint arXiv:2309.16463, 2023 - arxiv.org
We consider Shimura varieties associated to a unitary group of signature $(ns, s) $ where $
n $ is even. For these varieties, we construct smooth $ p $-adic integral models for $ s= 1 …
n $ is even. For these varieties, we construct smooth $ p $-adic integral models for $ s= 1 …
The canonicity of the integral models of RSZ Shimura varieties
Y Nakayama - arXiv preprint arXiv:2112.14558, 2021 - arxiv.org
We show that the integral models of Shimura varieties of Rapoport, Smithling and Zhang in
relation to variants of the arithmetic Gan-Gross-Prasad conjecture, the arithmetic …
relation to variants of the arithmetic Gan-Gross-Prasad conjecture, the arithmetic …
On Orthogonal Local Models of Hodge Type
I Zachos - International Mathematics Research Notices, 2023 - academic.oup.com
We study local models that describe the singularities of Shimura varieties of non-PEL type
for orthogonal groups at primes where the level subgroup is given by the stabilizer of a …
for orthogonal groups at primes where the level subgroup is given by the stabilizer of a …