Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I
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DOI: 10.1002/mana.201700415
Abstract: We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we provide a smooth solution (answer) to a conjecture… read more here.
Keywords: arbitrary unramified; varieties hodge; unramified mixed; mixed characteristic ... See more keywords
ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS
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DOI: 10.1017/fms.2019.10
Abstract: We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. We study their bi-algebraic systems, formulate… read more here.
Keywords: shimura varieties; mixed shimura; enlarged mixed; varieties algebraic ... See more keywords
Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties
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DOI: 10.1093/imrn/rny119
Abstract: We consider cycles on three-dimensional Shimura varieties attached to unitary groups, defined over extensions of a complex multiplication (CM) field $E$, which appear in the context of the conjectures of Gan et al. [6]. We… read more here.
Keywords: shimura varieties; vertical distribution; relations special; distribution relations ... See more keywords
Shimura varieties at level $\unicode[STIX]{x1D6E4}_{1}(p^{\infty })$ and Galois representations
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DOI: 10.1112/s0010437x20007149
Abstract: We show that the compactly supported cohomology of certain $\text{U}(n,n)$- or $\text{Sp}(2n)$-Shimura varieties with $\unicode[STIX]{x1D6E4}_{1}(p^{\infty })$-level vanishes above the middle degree. The only assumption is that we work over a CM field $F$ in which… read more here.
Keywords: x1d6e4 infty; shimura varieties; stix x1d6e4; unicode stix ... See more keywords
Arithmetic diagonal cycles on unitary Shimura varieties
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DOI: 10.1112/s0010437x20007289
Abstract: We define variants of PEL type of the Shimura varieties that appear in the context of the arithmetic Gan–Gross–Prasad (AGGP) conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global… read more here.
Keywords: unitary shimura; shimura varieties; arithmetic diagonal; shimura ... See more keywords