## Geometric Aspects of Dwork Theory, Volume 1This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of thep-adic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey articles written by leading experts in the field. The book willprovide an indispensable resource for all those wishing to approach the frontiers of research in arithmetic algebraic geometry. |

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### Contents

Alan Adolphson and Steven Sperber | 43 |

Mladen Dimitrov and Jacques Tilouine | 111 |

Fabrizio Andreatta and Eyal Z Goren | 113 |

Francesco Baldassarri and Pierre Berthelot | 177 |

Introduction to padic qdifference equations 615 | 243 |

Francesco Baldassarri and Andrea DAgnolo | 245 |

Vladimir G Berkovich | 293 |

JeanBenoît Bost | 372 |

Algebraicity criteria for smooth formal germs of subvarieties in algebraic varieties | 398 |

Gilles Christol | 419 |

Robert F Coleman and William A Stein | 437 |

Richard Crew | 451 |

462 | |

Jan Denefand François Loeser | 509 |

Mladen Dimitrov | 527 |

The canonical seminorm attached to a germ of analytic curve in a complex | 388 |