2 citations · 6 across the 7 of their papers we have counts for
7 papers
A higher Gross-Zagier type formula for moduli of shtukas at deeper level
Patrick Bieker
We generalize the function field analogue analogue of the Gross-Zagier and Waldspurger formulae due to Yun and Zhang relating the (higher) derivative of an automorphic (base change…
Normality of Schubert varieties in affine Grassmannians II: The tamely ramified case
Patrick Bieker
We prove a criterion for the normality of Schubert varieties in twisted affine Grassmannians in terms of the order of the algebraic fundamental group of a certain Levi subgroup, in…
A converse theorem for Borcherds products in signature
Patrick Bieker, Paul Kiefer
We show that a modular unit on two copies of the upper half-plane is a Borcherds product if and only if its boundary divisor is a special boundary divisor. Therefore, we define a s…
Normality of Schubert varieties in affine Grassmannians
Patrick Bieker, Timo Richarz
We classify all normal Schubert varieties in the affine Grassmannian of a semisimple group over an arbitrary field with special attention to small positive characteristic. The proo…
Integral models of moduli spaces of shtukas with deep Bruhat-Tits level structures
Patrick Bieker
We construct integral models for moduli spaces of shtukas with deep Bruhat-Tits level structures. We embed the moduli space of global shtukas for a deep Bruhat-Tits group scheme in…
Compactification of Level Maps of Moduli Spaces of Drinfeld Shtukas
Patrick Bieker
We define Drinfeld level structures for Drinfeld shtukas of any rank and show that their moduli spaces are regular and admit finite flat level maps. In particular, the moduli space…
Invariants for the Weil representation and Modular Units for Orthogonal Groups of Signature (2,2)
Patrick Bieker
We show that the space of invariants for the Weil representation for discriminant groups which contain self-dual isotropic subgroups is spanned by the characteristic functions of t…