Holmstrom Integral model

Schneider survey on the Beilinson conj, says that a proper flat model always exists, and the the image of motivic cohom of such a model is conjecturally independent of the choice of model. Also, the independence buy not the existence is known for regular proper models.

http://mathoverflow.net/questions/98825/existence-of-proper-integral-models

Check maybe Liu later chapters.

For regular models over DVRs, maybe something is in Liu, Gabber, Lorenzini

http://mathoverflow.net/questions/117179/global-minimal-model-over-a-non-affine-base

http://mathoverflow.net/questions/22998/is-there-a-deep-relationship-between-models-and-etale-cohomology-if-so-why-a

Bosch et al: Neron models, in Elliptic curve folder.

arXiv:0908.1831 Integral Models of Extremal Rational Elliptic Surfaces from arXiv Front: math.AG by Tyler J. Jarvis, William E. Lang, Jeremy R. Ricks Miranda and Persson classified all extremal rational elliptic surfaces in characteristic zero. We show that each surface in Miranda and Persson’s classification has an integral model with good reduction everywhere (except for those of type X_{11}(j), which is an exceptional case), and that every extremal rational elliptic surface over an algebraically closed field of characteristic p > 0 can be obtained by reducing one of these integral models mod p.

arXiv:0909.0969 Purity results for $p$-divisible groups and abelian schemes over regular bases of mixed characteristic from arXiv Front: math.AG by Adrian Vasiu, Thomas Zink Let $p$ be a prime. Let $(R,\ideal{m})$ be a regular local ring of mixed characteristic $(0,p)$ and absolute index of ramification $e$. We provide general criteria of when each abelian scheme over $\Spec R\setminus{\ideal{m}}$ extends to an abelian scheme over $\Spec R$. We show that such extensions always exist if $e\le p-1$, exist in most cases if $p\le e\le 2p-3$, and do not exist in general if $e\ge 2p-2$. The case $e\le p-1$ implies the uniqueness of integral canonical models of Shimura varieties over a discrete valuation ring $O$ of mixed characteristic $(0,p)$ and index of ramification at most $p-1$. This leads to large classes of examples of Néron models over $O$. If $p>2$ and index $p-1$, the examples are new.

arXiv:0707.1668 Good Reductions of Shimura Varieties of Hodge Type in Arbitrary Unramified Mixed Characteristic, Part I fra arXiv Front: math.NT av Adrian Vasiu 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 solve a conjecture of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic $(0,p)$ of integral canonical models of projective Shimura varieties of Hodge type; this forms progress towards the proof of conjectures of Milne and Reimann. Though the second application was known before in some cases, its proof is new and more of a principle.

nLab page on Integral model